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:

$$
LATEXBLOCK0
$$

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 \(y = 1\):

$$
LATEXBLOCK1
$$

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 \(y=1\)