Question

choose a method that can be used to solve this system of equations by elimination.
2x - 2y = 24
4x + 7y = -40
subtract 2x from both equations and solve the first equation for y
multiply the first equation by -2 and add the second equation.
add the first equation to the second equation and subtract 6x from both sides of the equation

Explanation:

To solve a system of linear equations by elimination, we aim to eliminate one variable. The first equation is \(2x - 2y = 24\), and the second is \(4x + 7y = -40\). If we multiply the first equation by -2, we get \(-4x + 4y = -48\). Now, adding this new equation to the second equation (\(4x + 7y = -40\)) will eliminate the \(x\) variable (\(-4x + 4x = 0\)), allowing us to solve for \(y\). The other options either don't eliminate a variable (like subtracting \(2x\) or adding the original equations and subtracting \(6x\)) or use substitution - like solving for \(y\) - rather than elimination.

Answer:

Multiply the first equation by -2 and add the second equation.