Question

Decide which variable to eliminate when using linear combinations to solve the system. Explain your thinking. $$\begin{aligned} &5 y-3 x=7\\\ &x+3 y=7 \end{aligned}$$

Short answer

It's more beneficial to eliminate the variable x because of its coefficients in the two equations. After eliminating x by adding the two equations, we solve the resulting equation for y. Finally, y's value is substituted back into the second equation to solve for x.

Step-by-step solution

Addition of the Two Equations

Add \(5y - 3x = 7\) and \(x + 3y = 7\) together. This way, the variable x in the two equations will cancel out, as the coefficients are oppositely signed.

Solve for y

Once the equations are summed, solve the resulting equation for y. Simplify the equation, and solve to find the exact value of y.

Substitute y into the second equation

Once y has been determined, substitute the value back into the second equation \(x + 3y = 7\) in the place of y, and solve for x.