A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[5x+2y=23],[5x+3y=32]:} Add to eliminate x. Subtract to eliminate x. Add to eliminate y. Subtract to eliminate y.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[5x+2y=23],[5x+3y=32]:} Add to eliminate  x. Subtract to eliminate  x. Add to eliminate  y. Subtract to eliminate  y.

Bytelearn · Accepted Answer

Analyze Coefficients: Analyze the coefficients of x and y in both equations. We have the system of equations: 5x + 2y = 23 5x + 3y = 32 To eliminate a variable, we need to make the coefficients of either x or y opposite in both equations so that when we add or subtract the equations, one variable cancels out.Compare Coefficients of x: Compare the coefficients of x in both equations. The coefficients of x in both equations are the same (5 and 5). This means we can eliminate x by subtracting one equation from the other.Compare Coefficients of y: Compare the coefficients of y in both equations. The coefficients of y are 2 and 3, which are not the same and not opposites, so we cannot directly eliminate y by adding or subtracting the equations without first multiplying one or both equations by a number to make the coefficients of y opposites.Decide on Operation: Decide on the operation to eliminate x. Since the coefficients of x are already the same, we can subtract the second equation from the first to eliminate x. (5x + 2y) - (5x + 3y) = 23 - 32 This will eliminate x because 5x - 5x = 0.

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