Question

solve the system of equations.
-5y - 10x = 45
-3y + 10x = -5
x =

y =

Explanation:

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

The two equations are:
\(-5y - 10x = 45\) (Equation 1)
\(-3y + 10x = -5\) (Equation 2)

Adding Equation 1 and Equation 2:
\[

$$\begin{align*} (-5y - 10x)+(-3y + 10x)&=45+(-5)\\ -5y - 10x - 3y + 10x&=40\\ -8y&=40 \end{align*}$$

\]

Step2: Solve for \(y\)

Divide both sides of \(-8y = 40\) by \(-8\):
\[
y=\frac{40}{-8}=-5
\]

Step3: Substitute \(y = -5\) into Equation 2 to solve for \(x\)

Substitute \(y=-5\) into \(-3y + 10x = -5\):
\[

$$\begin{align*} -3\times(-5)+10x&=-5\\ 15 + 10x&=-5 \end{align*}$$

\]
Subtract 15 from both sides:
\[
10x=-5 - 15=-20
\]
Divide both sides by 10:
\[
x=\frac{-20}{10}=-2
\]

Answer:

\(x = -2\), \(y = -5\)