Question

-5x - 6y = -26
5x - 3y = 17

Explanation:

Step1: Add the two equations to eliminate \(x\)

The first equation is \(-5x - 6y=-26\) and the second is \(5x - 3y = 17\). Adding them together:
\[

$$\begin{align*} (-5x - 6y)+(5x - 3y)&=-26 + 17\\ -5x+5x-6y - 3y&=-9\\ -9y&=-9 \end{align*}$$

\]

Step2: Solve for \(y\)

Divide both sides of \(-9y=-9\) by \(-9\):
\[y=\frac{-9}{-9} = 1\]

Step3: Substitute \(y = 1\) into one of the equations to solve for \(x\)

Let's use the second equation \(5x-3y = 17\). Substitute \(y = 1\):
\[

$$\begin{align*} 5x-3(1)&=17\\ 5x-3&=17\\ 5x&=17 + 3\\ 5x&=20 \end{align*}$$

\]

Step4: Solve for \(x\)

Divide both sides of \(5x = 20\) by \(5\):
\[x=\frac{20}{5}=4\]

Answer:

The solution to the system of equations is \(x = 4\) and \(y=1\)