Question

Choose a method to solve the linear system. Explain your choice, and then solve the system. $$ \begin{aligned} &-y=-4\\\ &x+2 y=4 \end{aligned} $$

Short answer

The solution to the system is \(\{x, y\} = \{-4, 4\}\).

Step-by-step solution

Choose a solution method

For this linear system, one can see that the first equation is already solved for \(y\). Thus, it's most efficient to use the substitution method for solving the system.

Apply the substitution method

From the first equation, one can see that \(y = 4\). Substitute \(y = 4\) into the second equation to solve for \(x\). Thus, the second equation simplifies to \(x + 2(4) = 4\), which results in \(x = -4\).

Verify the solution

The solution is \(\{x, y\} = \{-4, 4\}\). To verify it, substitute these values into both original equations. The first becomes \(-4 = -4\), and the second becomes \(-4 + 2(4) = 4\), verifying that both equations hold true with these solutions.