Question

find the solution of the system of equations. \\(\

$$\begin{cases} 5x - y = -30 \\\\ 4x + y = -15 \\end{cases}$$

\\) show your work here \\(x =\\) \\(y =\\) check

Explanation:

Step1: Add the two equations

Add the equations \(5x - y = -30\) and \(4x + y = -15\) to eliminate \(y\).
\((5x - y)+(4x + y)=-30+(-15)\)
Simplify the left side: \(5x - y + 4x + y = 9x\)
Simplify the right side: \(-30 - 15=-45\)
So we get \(9x=-45\)

Step2: Solve for \(x\)

Divide both sides of \(9x = -45\) by \(9\):
\(x=\frac{-45}{9}=-5\)

Step3: Substitute \(x = -5\) into one of the original equations

Let's substitute \(x=-5\) into the second equation \(4x + y=-15\)
\(4\times(-5)+y=-15\)
Calculate \(4\times(-5)=-20\), so the equation becomes \(-20 + y=-15\)

Step4: Solve for \(y\)

Add \(20\) to both sides of \(-20 + y=-15\):
\(y=-15 + 20 = 5\)

Answer:

\(x=-5\), \(y = 5\)