Solving with Elimination Quick Check
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Question
Solve the system of two equations using elimination with multiplication.
4x−6y=−48
−2x+4y=30(1 point)
Responses
(−3, 6)
left parenthesis negative 3 comma 6 right parenthesis
(3, 9)
left parenthesis 3 comma 9 right parenthesis
(−33,−9)
left parenthesis negative 33 comma negative 9 right parenthesis
(−21,−6)
left parenthesis negative 21 comma negative 6 right parenthesis
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To solve the system of equations using elimination with multiplication, we need to multiply one or both equations by a constant so that when we add the equations together, one of the variables will cancel out.
Let's start by multiplying the second equation by 2:
2(-2x + 4y) = 2(30)
-4x + 8y = 60
Now we can add the two equations together:
(4x - 6y) + (-4x + 8y) = -48 + 60
2y = 12
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:
4x - 6(6) = -48
4x - 36 = -48
4x = -12
x = -3
Therefore, the solution to the system of equations is (-3, 6).
Answer: (−3, 6)