Solve the system of equations using the elimination method:

1. \(4x + 12 = -7y\)
2. \(-y + 12 = 4x\)

Take the second equation and flip it around so the y on the left ends up on the right and the 4x on the right ends up on the left. This makes all negatives positive and all positives negative. -4x + 12 = y
Then add the first equation to the second equation 4x +12 = -7y -4x + 12 = y this eliminates the x's 24 = - 6y then divide by - 6 - 6 - 6 - 4 = y
So if you know that y = negative 4, you can substitute into either equation. I pick the second one because I am a lazy person. -y + 12 = 4 x -(-4) + 12 = 4 x combine your numbers 16 = 4 x then divide by 4 4 = x So your solution is: x = 4 and y = -4 or this is also written (4, -4)
Does that work for you?

Answered by anitajoharder | 2024-06-10

{ 4 x + 12 = − 7 y − y + 12 = 4 x ​ { 4 x + 7 y = − 12 − 4 x − y = − 12 ​ + − − − − − − − 6 y = − 24 / : 6 y = − 6 24 ​ y = − 4
4 x + 12 = − 7 y 4 x + 12 = − 7 ∗ ( − 4 ) 4 x = 28 − 12 4 x = 16 / : 4 x = 4 16 ​ x = 4 { x = 4 y = − 4 ​

Answered by Lilith | 2024-06-10

Using the elimination method, we found the solution to the system of equations to be (4, -4). We substituted expressions to eliminate variables and calculated each step carefully. Therefore, the intersection point of the two equations is at (4, -4).
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Answered by anitajoharder | 2024-12-24