\begin{tabular}{l} Solve using substitution. \ $$ \qquad \begin{array}{l}y=-5 x+8 \ y=-2 x+5\end{array} $$ \ \hline\end{tabular}

Question

UpStudy AI · Accepted Answer

1. We are given the system of equations:
   $$
   y = -5x + 8
   $$
   $$
   y = -2x + 5
   $$

2. Since both expressions equal $$ y $$, we set them equal to each other:
   $$
   -5x + 8 = -2x + 5
   $$

3. To solve for $$ x $$, add $$ 5x $$ to both sides:
   $$
   8 = 3x + 5
   $$

4. Subtract $$ 5 $$ from both sides:
   $$
   3 = 3x
   $$

5. Divide both sides by $$ 3 $$:
   $$
   x = 1
   $$

6. Substitute $$ x = 1 $$ into one of the original equations; using $$ y = -5x + 8 $$:
   $$
   y = -5(1) + 8 = -5 + 8 = 3
   $$

7. The solution to the system is:
   $$
   (x, y) = (1, 3)
   $$
The solution is $$ x = 1 $$ and $$ y = 3 $$.

\begin{tabular}{l} Solve using substitution. \\ \( \qquad \begin{array}{l}y=-5 x+8 \\ y=-2 x+5\end{array} \) \\ \hline\end{tabular}