Question


Solving with Elimination Practice
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1 of 51 of 5 Items
Question
Solve the system of equations.
6x–5y=27
3x+5y=36 (1 point)
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,
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Answer
Solve the system of equations.
2x+8y=8
2x−4y=−16 (1 point)
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,
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Answer
Solve the system of equations.
7x+3y=−25
−7x+9y=−47(1 point)
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,
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Answer
Solve the system of equations.
–x+6y=13
4x–10y=–10 (1 point)
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,
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Answer
Solve the system of equations.
3x+6y=21
–5x+2y=13(1 point)
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Answered by GPT 3.5
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).
Answered by GPT 3.5
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).
Answered by GPT 3.5
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).
Answered by GPT 3.5
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).
Answered by GPT 3.5
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).