A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[-10 x-y=-30],[10 x+2y=40]:} Subtract to eliminate y. Subtract to eliminate x. Add to eliminate y. Add to eliminate x.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[-10 x-y=-30],[10 x+2y=40]:} Subtract to eliminate  y. Subtract to eliminate  x. Add to eliminate  y. Add to eliminate  x.

Bytelearn · Accepted Answer

Given System of Equations: We are given the system of equations: {-10x - y = -30, 10x + 2y = 40} To eliminate a variable, we look for coefficients that are opposites or can be made into opposites. Here, we notice that the coefficients of x in both equations are -10 and 10, which are already opposites.Identifying Opposite Coefficients: Since the coefficients of x are opposites, we can add the two equations together to eliminate the x variable. This is because (-10x) + (10x) equals 0, effectively removing the x variable from the equation.Eliminating x Variable: Let's add the two equations: (-10x - y) + (10x + 2y) = -30 + 40 -10x + 10x - y + 2y = 10 0x + y = 10 This simplifies to y = 10.

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