\( \begin{array}{l}5 x+2 y=8 \\ x+y=4 \\ \text { If you want to solve the system of equations by addition, which of the following could you do? } \\ \text { Multiply the second equation by }-2 \text { and add. } \\ \text { Multiply the second equation by } 5 \text { and add. } \\ \text { Multiply the second equation by } 2 \text { and add. }\end{array} . \begin{array}{l}\end{array} \).

To solve the system of equations using the addition method (also known as the elimination method), the key is to make the coefficients of one of the variables equal so that they can be eliminated when the equations are added. Multiplying the second equation \(x + y = 4\) by -2 transforms it to \(-2x - 2y = -8\). When you add this to the first equation \(5x + 2y = 8\), the \(y\) terms cancel out, enabling you to solve for \(x\) easily. Alternatively, if you multiplied the second equation by 5, you would get \(5x + 5y = 20\). Adding this to the first equation would complicate things instead of simplifying them since you’d still have both variables present. The best choice for elimination is to target coefficients that will cancel out effectively!