Solve the following system of equations to find 𝑥. 6𝑥−3𝑦=−48 6𝑥+9𝑦=−24 Group of answer choices𝑥=3 𝑥=−2 𝑥=2 𝑥=7 𝑥=−7
Question
Solve the following system of equations to find 𝑥. 6𝑥−3𝑦=−48 6𝑥+9𝑦=−24 Group of answer choices𝑥=3 𝑥=−2 𝑥=2 𝑥=7 𝑥=−7
Solution
To solve the system of equations for x, follow these steps:
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Write down the system of equations:
6x - 3y = -48 6x + 9y = -24
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To eliminate one of the variables, subtract the second equation from the first:
(6x - 3y) - (6x + 9y) = -48 - (-24)
This simplifies to:
-12y = -24
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Solve for y by dividing both sides of the equation by -12:
y = -24 / -12 = 2
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Substitute y = 2 into the first equation:
6x - 3*2 = -48
This simplifies to:
6x - 6 = -48
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Add 6 to both sides of the equation to isolate 6x:
6x = -48 + 6 = -42
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Divide both sides of the equation by 6 to solve for x:
x = -42 / 6 = -7
So, the solution to the system of equations is x = -7.
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