A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[-5x-10 y=-140],[-5x-3y=-77]:} Add to eliminate y. Subtract to eliminate x. Add to eliminate x. Subtract to eliminate y.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[-5x-10 y=-140],[-5x-3y=-77]:} Add to eliminate  y. Subtract to eliminate  x. Add to eliminate  x. Subtract to eliminate  y.

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Given Equations: We are given the system of equations: 1) -5x - 10y = -140 2) -5x - 3y = -77  To eliminate a variable, we need to make the coefficients of either x or y the same in both equations, so that when we add or subtract the equations, one of the variables cancels out. In this case, the coefficients of x are already the same in both equations (-5). Therefore, we can eliminate x by adding the two equations together.  Adding the two equations: (-5x - 10y) + (-5x - 3y) = -140 + -77 -5x - 5x - 10y - 3y = -140 - 77 -10x - 13y = -217  However, this does not eliminate x, as we have not correctly combined like terms. The correct combination should be: -5x - 5x = -10x (for the x terms) -10y - 3y = -13y (for the y terms)  Let's correct this and add the equations again: (-5x - 10y) + (-5x - 3y) = -140 + -77 -5x + (-5x) - 10y - 3y = -140 - 77 -10x - 13y = -217  This is incorrect because we have not eliminated any variable; we have simply combined the two equations incorrectly. The correct step to eliminate x would be to add the two equations directly without changing any coefficients since they are already the same for x.  Let's add the equations correctly: (-5x - 10y) + (-5x - 3y) = -140 + -77 -5x + (-5x) = -10x (for the x terms, which cancel each other out) -10y + (-3y) = -13y (for the y terms)  The correct addition is: 0x - 13y = -217  This shows that adding the two equations will eliminate x.

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