A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. {:[8x+7y=92],[-8x-6y=-88]:} 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.  {:[8x+7y=92],[-8x-6y=-88]:} Subtract to eliminate  y. Subtract to eliminate  x. Add to eliminate  y. Add to eliminate  x.

Bytelearn · Accepted Answer

Analyze Variables: Analyze the system of equations to determine which variable can be eliminated with the least amount of effort. The system of equations is: $$ \begin{cases}  8x + 7y = 92 \ -8x - 6y = -88  \end{cases} $$ We can see that the coefficients of $x$ in both equations are $8$ and $-8$, which are opposites of each other. This means that adding the two equations will eliminate the $x$ variable.Eliminate x: Perform the operation to eliminate the $x$ variable. Adding the two equations: $$ (8x + 7y) + (-8x - 6y) = 92 + (-88) $$ $$ 8x - 8x + 7y - 6y = 92 - 88 $$ $$ 0x + y = 4 $$ The $x$ variable has been successfully eliminated.

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