Question

solve the system of equations.$\begin{cases}x = 5y - 13 \\x = -2y + 1end{cases}$

Explanation:

Step1: Set equations equal

Since both expressions equal $x$, set them equal to each other:
$5y - 13 = -2y + 1$

Step2: Isolate $y$ terms

Add $2y$ to both sides:
$5y + 2y - 13 = 1$
$7y - 13 = 1$

Step3: Solve for $y$

Add 13 to both sides, then divide by 7:
$7y = 1 + 13$
$7y = 14$
$y = \frac{14}{7} = 2$

Step4: Substitute $y$ to find $x$

Use $x = 5y - 13$:
$x = 5(2) - 13 = 10 - 13 = -3$

Answer:

$x=-3$, $y=2$