Question

solve the system of equations.
2y - 3x = -27
5y + 3x = 6
x =
y =

Explanation:

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

The two equations are:
\(2y - 3x = -27\) (Equation 1)
\(5y + 3x = 6\) (Equation 2)

Adding Equation 1 and Equation 2:
\((2y - 3x)+(5y + 3x)=-27 + 6\)
Simplify the left side: \(2y+5y-3x + 3x=7y\)
Simplify the right side: \(-21\)
So we get \(7y=-21\)

Step2: Solve for \(y\)

From \(7y=-21\), divide both sides by 7:
\(y=\frac{-21}{7}=-3\)

Step3: Substitute \(y = - 3\) into one of the original equations to solve for \(x\)

Let's substitute into Equation 2: \(5y+3x = 6\)
Substitute \(y=-3\):
\(5\times(-3)+3x = 6\)
Simplify: \(-15 + 3x=6\)
Add 15 to both sides: \(3x=6 + 15=21\)
Divide both sides by 3: \(x=\frac{21}{3}=7\)

Answer:

\(x = 7\)
\(y=-3\)