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:

$$
LATEXBLOCK0
$$

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

$$
LATEXBLOCK1
$$

Subtract 15 from both sides:

$$ 10x=-5 - 15=-20 $$

Divide both sides by 10:

$$ x=\frac{-20}{10}=-2 $$

Answer:

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