Question

find the solution of the system of equations.
3x + 3y = 42
x - 3y = -22

Explanation:

Step1: Add the two equations

Add the equations \(3x + 3y = 42\) and \(x - 3y = -22\) together. This will eliminate the \(y\) term.
\((3x + 3y)+(x - 3y)=42+(-22)\)
Simplify the left side: \(3x + 3y + x - 3y = 4x\)
Simplify the right side: \(42 - 22 = 20\)
So we get \(4x = 20\)

Step2: Solve for x

Divide both sides of \(4x = 20\) by 4.
\(x=\frac{20}{4}=5\)

Step3: Substitute x into one equation

Substitute \(x = 5\) into the second equation \(x - 3y = -22\).
\(5 - 3y = -22\)

Step4: Solve for y

Subtract 5 from both sides: \(-3y=-22 - 5=-27\)
Divide both sides by -3: \(y=\frac{-27}{-3}=9\)

Answer:

The solution to the system is \(x = 5\) and \(y = 9\)