Solving with Elimination Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Solve the system of equations.
6x–5y=27
3x+5y=36 (1 point)
(
,
)

Answer 1

To solve this system of equations, we can use the method of elimination. Adding the two equations together, we get:

(6x - 5y) + (3x + 5y) = 27 + 36
9x = 63
x = 7

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = 3

Therefore, the solution to the system of equations is (7, 3).

Answer 2

Solve the system of equations.
2x+8y=8
2x−4y=−16 (1 point)
(
,
)

Answer 3

To solve this system of equations using the elimination method, we can start by subtracting the second equation from the first in order to eliminate the term 2x:

(2x + 8y) - (2x - 4y) = 8 - (-16)
12y = 24
y = 2

Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

2x + 8(2) = 8
2x + 16 = 8
2x = -8
x = -4

Therefore, the solution to the system of equations is (-4, 2).

Answer 4

Solve the system of equations.
7x+3y=−25
−7x+9y=−47(1 point)
(
,
)

Answer 5

To solve this system of equations using the elimination method, we can add the two equations together in order to eliminate the term 7x:

(7x + 3y) + (-7x + 9y) = -25 + (-47)
12y = -72
y = -6

Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

7x + 3(-6) = -25
7x - 18 = -25
7x = -7
x = -1

Therefore, the solution to the system of equations is (-1, -6).

Answer 6

Solve the system of equations.
–x+6y=13
4x–10y=–10 (1 point)
(
,
)

Answer 7

To solve this system of equations using the elimination method, we can multiply the first equation by 4 in order to eliminate the x terms:

-4x + 24y = 52
4x - 10y = -10

Now, we can add the two equations together to eliminate the x terms:

-4x + 24y + 4x - 10y = 52 - 10
14y = 42
y = 3

Now, we can substitute the value of y back into one of the original equations. Let's use the first equation:

-x + 6(3) = 13
-x + 18 = 13
-x = -5
x = 5

Therefore, the solution to the system of equations is (5, 3).

Answer 8

Solve the system of equations.
3x+6y=21
–5x+2y=13(1 point)
(
,
)

Answer 9

To solve this system of equations using the elimination method, we can multiply the first equation by 5 and the second equation by 3 in order to eliminate the x terms:

15x + 30y = 105
-15x + 6y = 39

Now, we can add the two equations together to eliminate the x terms:

15x + 30y + (-15x + 6y) = 105 + 39
36y = 144
y = 4

Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

3x + 6(4) = 21
3x + 24 = 21
3x = -3
x = -1

Therefore, the solution to the system of equations is (-1, 4).