Question

find the solution of the system of equations.
-6x - 10y = -18
-3x + 10y = 36

Explanation:

Step1: Eliminate \( y \) by adding equations

Add the two equations: \((-6x - 10y)+(-3x + 10y)=-18 + 36\)
Simplify: \(-9x=18\)

Step2: Solve for \( x \)

Divide both sides by \(-9\): \(x=\frac{18}{-9}=-2\)

Step3: Substitute \( x = -2 \) into one equation (e.g., \(-3x + 10y = 36\))

Substitute: \(-3(-2)+10y = 36\)
Simplify: \(6 + 10y = 36\)

Step4: Solve for \( y \)

Subtract 6: \(10y = 36 - 6 = 30\)
Divide by 10: \(y=\frac{30}{10}=3\)

Answer:

\( x = -2 \), \( y = 3 \)