Question

variables are not aligned. rearrange first! eliminate and make sure your solution is in the correct order.
system
\

$$\begin{cases}x - 5y = 13\\\\9y - x = -17\\end{cases}$$

(\quad,\quad)
\

$$\begin{cases}6x - y = 3\\\\3y - 6x = 15\\end{cases}$$

(\quad,\quad)
solution

Explanation:

Step1: Rearrange first system

$$\begin{cases} x - 5y = 13 \\ -x + 9y = -17 \end{cases}$$

Step2: Add equations to eliminate $x$

$ (x - 5y) + (-x + 9y) = 13 + (-17) $
$4y = -4$

Step3: Solve for $y$

$y = \frac{-4}{4} = -1$

Step4: Substitute $y=-1$ into $x-5y=13$

$x - 5(-1) = 13$
$x + 5 = 13$
$x = 13 - 5 = 8$

Step5: Rearrange second system

$$\begin{cases} 6x - y = 3 \\ -6x + 3y = 15 \end{cases}$$

Step6: Add equations to eliminate $x$

$ (6x - y) + (-6x + 3y) = 3 + 15 $
$2y = 18$

Step7: Solve for $y$

$y = \frac{18}{2} = 9$

Step8: Substitute $y=9$ into $6x-y=3$

$6x - 9 = 3$
$6x = 3 + 9 = 12$
$x = \frac{12}{6} = 2$

Answer:

First system solution: $(8, -1)$
Second system solution: $(2, 9)$