Solve the following system of equations graphically on the set of axes below. y=3x−3 , x+y=5
Answers
Answer:
x=2, y=3
Step-by-step explanation:
First, graph both equations on a rectangular coordinate system (see attached screenshot). Then, simply figure out where these two lines intersect. Since they intersect at (2,3), x=2 and y=3.
Plugging these values in the equations for x and y, you can see if these are the correct answers:
(3)=3(2)-3, (2)+(3)=5
Since both of these are true, you have the right answer.
Hope this helps!
Two linear equation has their solutions on the points where they intersect each other.
The solution of the given system of equations is:
x = 2, y = 3.
How to determine the solution of system of linear equations graphically?Each linear equation represents a straight line.
If both the given lines intersect at one point, then that point's coordinate is the solution of the given system of the equations.
If both the given lines are parallel, then there is no intersection and thus no solution.
If both the lines are coincident(that is, lying over each other fully), then there are infinite points of intersection, as they touch each other on infinite points, and thus infinite solutions to the given system of equations exist.
Using method of substitution to solve the system of equations:[tex]y = 3x-3\\ x+y = 5 [/tex]
Substituting the value of y from first equation in the second equation, we get:
[tex]x + y = 5\\ x + (3x-3) = 5\\ x+3x = 5+3\\ 4x = 8 \\ x = 2\\ [/tex]
Thus, putting this value of x in first equation, we get:
[tex]y = 3x - 3\\ y = 3 \times 2 - 3\\ y = 6-3\\ y = 3[/tex]
Thus, the system has one solution and it is x = 2, y = 3.
Using graphing, we can see that point of intersection is (x,y) = (2,3)
Learn more about solutions of system of linear equations:
https://brainly.com/question/9351049
Related Questions
another question
3c+5c+2=18
Solving Multi-Step Equations by Combining Like Terms
Answers
Answer: c=2
Step-by-step explanation:
help me please I don't understand
Answers
Answer:
1, not a function because the -2 x repeats it's self twice, and only y functions can repeat
2, yes it is because it is a straight line and none of the x functions repeat
3, yes because none of the x functions repeat
4, yes because all the x functions only have one y function
5, no because 16x repeats
6, no because 2x goes to the same number twice
Step-by-step explanation:
Which question can be answered using the expression 1/3÷ 3/4
Answers
Answer:
Jillian had a cake and Ruby ate 2/3 of it. Jillian's friends then came over and consumed 3/4 of the kuchen, which Ruby already ate out of. How much of the cake is left?
Step-by-step explanation:
Just think about it with simpler numbers. What if the expression was (4 ÷ 2)? Then the word problem could be made quite easily. Following the previous example, simply replace the numbers (4 and 2) with the fractions given (1/3 and 3/4) and make a few tweaks for it to make more sense.
Good luck!
The total pizza left is 1/3 of the whole pizza. If the remainig student are to take 3/4 of the remaining, how much will each student take
Word problems involving equationsAlgebraic equations are ways we can solve real life apllications.
Given the division problem
1/3÷ 3/4
This can be written usng this statement:
The total pizza left is 1/3 of the whole pizza. If the remainig student are to take 3/4 of the remaining, how much will each student take
Learn more on word problem here: https://brainly.com/question/21405634
#SPJ2
y/-8 = 1/16
find y. thank you!
Answers
Answer:
-0.5
Step-by-step explanation:
The answer is -0.5. We know this because with fractions you can multiply the top and bottom to make them = each other. we multiply the 8 by 2 to get -16. and we need the top to be half of 1 so 0.5. the 0.5 needs to be negative so they can = a positive in the final equation.
The perimeter of a kite can be found using the formula P = 2S + 2L. Which equation expresses S in terms of P and L?
Group of answer choices
a. S = 1/2p - L
b. S = 1/2p+L
c . S=1/2p+2L
d. S = 1/2p-2L
Answers
Answer:
The answer is AA. S = 1/2p - LStep-by-step explanation:
Step one:
given the perimeter function
P = 2S + 2L
we are expected in this problem to change the subject of the formula to S
Step two:
firstly, let us isolate the term that has S
2S=P-2L
divide both sides by 2
2S/2= (P-2L)/2
S=P/2-L
S = 1/2p - L
simple question just answer correctly to get brainleist and 10 pts! :)
Answers
Answer:
im pretty sure the answer is either a or c because. if i had to choose one though i'd probably go with C
Step-by-step explanation:
a function is a y for every x and im pretty sure both a and c display that, but a is going to all of numbers in the other bubble and there arent any other letters in the first one. hope this helps
please help me with this
Answers
Answer:
i dont really know sorry
Step-by-step explanation:
Help pls I'm gonna be screwed if you don't get this pls pls pls anyone who knows math well pls help me I'm gonna cry it's over due please:( :(
Just last two please
Answers
Answer:
WRONG ALL
Step-by-step explanation:
3. Should be:
[tex] - 4 \frac{7}{8} \times \frac{2}{3} \\ \\ - \frac{39}{8} \times \frac{2}{3} \\ \\ \frac{ -13}{4} [/tex]
4. Should be:
[tex] - 3 \frac{1}{5} + - \frac{2}{3} \\ \\ - 3 \frac{3}{15} - \frac{10}{15} \\ \\ - 3 \frac{7}{15} [/tex]
I hope this helps you :)
Right answer will get brainlist
Answers
Answer:
Step-by-step explanation:
1). b = 0
2). b = 5
3). b = 5
4). b = 5
Please answer...
Tracy has $35 to buy comic books and to pay for a single movie ticket. It costs $3 per comic book. The movie ticket costs $10. Which inequality can be used to determine how many comic books, b, Tracy can buy?
A: 3b + 10 >= 35
B: 10b + 3 >= 35
C: 3b + 10 <= 35
D: 10b + 3 <= 35
Answers
Answer ASAP PLZZ!!!!
Answers
Answer: m∠HIJ = m∠IHK because they are alternate interior angles
Step-by-step explanation:
Select the correct answer.
If the graph of f(x) = x is shifted up 9 units, what would be the equation of the new graph?
O A. g(x) = 9f()
B. g(x) = 9 - f()
Oc. g(x)
g() = f(x) +9
o(t) = f(x)
= - 9
D.
Answers
Answer:
b. g (x) = 9f (0)
Step-by-step explanation:
Item 8 A container has peppermint gum and spearmint gum. There are 18 pieces of peppermint gum in the container and the ratio of peppermint gum to spearmint gum is 2 : 3. Find the number of pieces of spearmint gum in the container.
Answers
Answer:Number of Spearmint gum = 27 pieces
Step-by-step explanation:
step 1
Let the total number of peppermint gum and spearmint gum in the container = X
Ratio of peppermint gum to spearmint gum= 2 : 3.
Total ratio = 2+ 3=5
Step 2
we were given that peppermint gum= 18 pieces , so total number of gums will be calculated as
Ratio of peppermint/ Total ratio x Total number of gums = Number of peppermint
2/5 x X= 18
X=(18X 5) / 2 = 45
X= Total number of gums = 45
Number of spearmint gum will now be
Ratio of spearmint/ Total ratio x Total number of gums = Number of spearmint
3/5 x 45= 27
Therefore Number of Spearmint gum = 27 pieces
can someone help me with these questions please?! -1.2x = 12 and
x/9 = 4
Answers
Answer:
Step-by-step explanation:
-1.2x=12 divide both sides by -1.2 to get x alone
x= 10
x/9=4 multiply both sides by 9
x=36
(3.0 x 10^-2)(7.2 x10^8)
Answers
Answer:
the answer is 21600000
Step-by-step explanation:
Please help with the picture below.
Answers
explanation: they are complementary angles, meaning they are the same. since a line adds up to 180°, take 128° away from 180° and you get 52°
Bus A and Bus B leave the bus depot at 2 pm.
Bus A takes 15 minutes to complete its route once and bus B takes 25 minutes to complete its
route once.
If both buses continue to repeat their route, at what time will they be back at the bus depot
together?
Assume the buses have no breaks in between routes.
Give your answer as a 12-hour clock time.
Answers
Answer:
LCM(30, 35) = 210 minutes.
The 2 Buses will be back at the depot 210 minutes after 5pm, or 5pm + 210 minutes =5 + 3.5 hours =8:30pm
Answer:
4:30 PM
Step-by-step explanation:
Bus A will meet Bus B on it's 10th route at 150 min. Bus B will meet Bus A at its 6th route at 150 min. 150 is also 2 hours and 30 min so they will meet at 4:30 PM.
HELPPPPPPP PLEASEEE
just answer 3-10
Answers
Answer:
Step-by-step explanation:
3). [tex]x=4,2[/tex]
4). [tex]x=7,-2[/tex]
5).[tex]x=-2±2i\sqrt{2}[/tex]
if the class sizes in a school vary from 22 to 30, what is the range?
Answers
Answer:
8 im pretty sure
Step-by-step explanation:
the sum of two numbers is 100 and their difference is 80, what are the two numbers
Answers
Answer:
The numbers are 90 and 10.
Step-by-step explanation:
Let the two numbers are x and y.
It has been given that sum of two numbers is 100. Hence, we have the equation,
x + y = 100 .........(i)
Now, the difference of these two numbers is 80. Thus, second equation is
x - y = 180......(ii)
Add equation (i) and (ii)
x + y + x - y = 100 + 80
2x = 180
Divide both sides by 2
x = 90
Substitute this value in (i)
90 + y = 100
y = 100- 90
y = 10
Therefore, the numbers are 90 and 10.
#Learn More:
The sum of two numbers is 450 and the smaller number is 120. What is the product?
Step-by-step explanation:
90 and 10x=90
y=10
Explanation:
Let x be equal to the first number.
Let y be equal to the second number.
We know that the sum of the two numbers is 100, so we can say that x+y=100.
We also know that the difference of the two numbers is 80, so we can also say that x-y=80
And now we have our two equations:
x+y=100
x-y=80
To find x and y, we first solve for one of the variables and plug it into one of the two equations to solve for the other. In this case, the easiest way to approach this question is to add both of the equations to cancel y out and solve for x (please check the picture attached for a better representation).
x+y=100
x-y=80
-> 2x=180
2x=180
Divide both sides by 2
2x/2=180/2
x=90
Now that we have found the value of the first number, x, we can plug it in to either of our two original equations to solve for y.
x+y=100
90+y=100
Subtract both sides by 90
90+y-90=100-90
y=10
Therefore, the value of x is 90 and the value of y is 10. Their sum is 100 and their difference is 80.
I hope this helps!
There are 8 puppies in a litter of Lab puppies. 5 of them are chocolate colored. What percent of the puppies are NOT chocolate-colored?
Answers
3/8 is not colored and then just divide 3-8 which would be 37.5, round 38%
Answer:
37.5
Step-by-step explanation:
It is really a simple equation, you are only dividing.
Hope this helps! ;)
Ilona is at a friend's home that is several miles from her home. She starts walking at a constant rate in a straight line toward her home. The expression -2t+10 gives the distance in miles that Ilona is from her home after t hours
Answers
Complete question is;
Ilona is at a friends home that is several miles from her home. She starts walking at a constant rate in a straight line toward her home.
The expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours. Select True or False for each of the following.
1. The friends home is 10 miles from Ilonas home
2. The distance Ilona has walked away from her friends home after t hours is given by the absolute value of -2t
3.The negative sign in the term indicates that Ilona is walking toward her home
4. Ilona is walking at a rate of 10 miles per hour
Answer:
Statements 1 & 2 are correct.
Step-by-step explanation:
We are told that the expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours.
Now, we know that distance = speed x time
Now, from the expression -2t + 10
It's clear that 2t is a distance value.
This means that the speed used in going home is 2 miles/hr
This means that at t hours, she has walked 2t miles from her friends home.
Thus, statement 2 is true because an absolute value of -2t will be 2t.
Since 2t is subtracted from 10 in the expression and 2t is the distance she has walked from her friends house at Time, t. It means that 10 miles is the distance from her friends house to her house.
Thus, statement 1 is also true
what must be considered in transplanting verbal phrases to mathematical phrases???
Answers
Answer:
addition, subtraction, division, multiply
When it is about 68°F, crickets chirp 124 times a minute. When it is about 80°F, they chirp 172 times a minute. WRITE an equation in POINT SLOPE FORM for the line that models this situation.
Answers
Answer:
4x+148
Step-by-step explanation:
Let the temperature be x and time taken by cricket to chirp be y
if when it is about 68°F, crickets chirp 124 times a minute, this means;
at x1 = 68, y1 = 124
If it is about 80°F, they chirp 172 times a minute, then;
at x2 = 80, y2 = 172
The standard form of equation in point slope form is expressed as;
y-y0 = m(x-x0)
m is the slope
(x0, y0) is a point on the line.
First we need to get the slope.
m = y2-y1/x2-x1
m = 172-124/80-68
m = 48/12
m =4
Substitute m = 4 and any point into the expression above. Using the coordinate (68, 124)
get the intercept c
124 = 4(68) + c
c = 272-124
c = 148
The required equation is expressed as y = 4x+148 OR y - 124 = 4(x-68)
Which is a linear function
A. f(x)=x+2
B. F(x)=x to the power of 2
C. F(x)=2 to the power of x
D. F(x)= |2x|
Answers
A. f(x)=x+2 is a linear function.
Answer:
A
Step-by-step explanation:
A is a linear function because, x^2 would be a parabola, 2^x would also result in a parabola, and |2x| would be a v shape.
Please help!!!! i appreciate math related answers pleaseeee
Answers
Answer:
7,802,000,000
Step-by-step explanation:
subtract: 1,020,000,000 - 239,800,000
how would I do 3(7/5x+4)
Answers
Answer: 21/5x+12
Step-by-step explanation:
3*7/5x+3*4
21/5x+12
1 and 3/4 times 1 and 1/3
Answers
Answer:
7/3
Step-by-step explanation:
Simplify the following:
(1 + 3/4) (1 + 1/3)
Hint: | Put the fractions in 1 + 1/3 over a common denominator.
Put 1 + 1/3 over the common denominator 3. 1 + 1/3 = 3/3 + 1/3:
(1 + 3/4) 3/3 + 1/3
Hint: | Add the fractions over a common denominator to a single fraction.
3/3 + 1/3 = (3 + 1)/3:
(1 + 3/4) (3 + 1)/3
Hint: | Evaluate 3 + 1.
3 + 1 = 4:
(1 + 3/4)×4/3
Hint: | Put the fractions in 1 + 3/4 over a common denominator.
Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:
4/3 4/4 + 3/4
Hint: | Add the fractions over a common denominator to a single fraction.
4/4 + 3/4 = (4 + 3)/4:
4/3 (4 + 3)/4
Hint: | Evaluate 4 + 3.
4 + 3 = 7:
7/4×4/3
Hint: | Express 7/4×4/3 as a single fraction.
7/4×4/3 = (7×4)/(4×3):
(7×4)/(4×3)
Hint: | Cancel common terms in the numerator and denominator of (7×4)/(4×3).
(7×4)/(4×3) = 4/4×7/3 = 7/3:
Answer: 7/3
Answer:
1 3/4 multiplied by 1 1/3 is 1 1/12
The original price for the sweater is $80. Today it is on sale for 30% off. What is the sale price for the sweater?
Answers
Answer:
56
Step-by-step explanation:
30 percent of 80 is 24, subtract
Answer:
56
Step-by-step explanation:
8 x .7=56
you get .7 by subtracting the 30 percent or .3 from the original price
The table below represents the number of hours a student worked and the amount of money the student earned. Determine the number of dollars the student would earn for working 40 hours. Explain how you arrived at your answer. ( I’ll PAY YOU 30 DOLLARS IN CASHAPP RIGHT NOW WHEN YOU DO IT)
Answers
Answer:
7.50
Step-by-step explanation:
45.00 divided by 6 = 7.5 or 7.50 income/hours worked
no cash needed hope it helps
