A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[5x-7y=-58],[-9x+7y=54]:} Subtract to eliminate y. Add to eliminate x. Subtract to eliminate x. Add to eliminate y.

Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.  {:[5x-7y=-58],[-9x+7y=54]:} Subtract to eliminate  y. Add to eliminate  x. Subtract to eliminate  x. Add to eliminate  y.

Bytelearn · Accepted Answer

Given System of Equations: We are given the system of equations: $$ \begin{cases} 5x - 7y = -58 \ -9x + 7y = 54 \end{cases} $$ To eliminate a variable, we look for coefficients that are the same or opposites. Here, the coefficients of $ y $ are $ -7 $ and $ 7 $, which are opposites. Therefore, we can eliminate $ y $ by adding the two equations together.Eliminate Variable by Addition: Perform the addition of the two equations: $$ (5x - 7y) + (-9x + 7y) = -58 + 54 $$ $$ 5x - 9x = -4 $$ $$ -7y + 7y = 0 $$ $$ -58 + 54 = -4 $$ The $ y $ terms cancel out, and we are left with: $$ -4x = -4 $$Confirmation of Correct Step: We can see that adding the two equations eliminates $ y $ and gives us an equation with only $ x $. This confirms that adding the two equations is the correct first step to eliminate $ y $.

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