A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[-8x+7y=30],[4x-7y=-22]:} Add to eliminate x. Subtract to eliminate y. Add to eliminate y. Subtract to eliminate x.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[-8x+7y=30],[4x-7y=-22]:} Add to eliminate  x. Subtract to eliminate  y. Add to eliminate  y. Subtract to eliminate  x.

Bytelearn · Accepted Answer

Identify Opposite Coefficients: We have the system of equations: -8x + 7y = 30 4x - 7y = -22 To eliminate a variable, we look for coefficients that are opposites or can be made into opposites. Here, we notice that the coefficients of y are 7 and -7, which are already opposites.Add Equations to Eliminate y: Since the coefficients of y are opposites, we can add the two equations together to eliminate y. The addition will result in the y terms canceling each other out. (-8x + 7y) + (4x - 7y) = 30 + (-22)Perform Addition and Simplify: Performing the addition, we get: -8x + 4x + 7y - 7y = 30 - 22 -4x = 8 This shows that adding the two equations eliminates y.

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