Question

solve the system by the addition method.
3x + 3y = 15
3x - 3y = 3

Explanation:

Step1: Add the two equations

Add the left - hand sides and the right - hand sides of the equations \(3x + 3y=15\) and \(3x - 3y = 3\) together.
\((3x+3y)+(3x - 3y)=15 + 3\)
Simplify the left - hand side: \(3x+3y+3x - 3y=6x\), and the right - hand side: \(15 + 3=18\). So we get the equation \(6x=18\).

Step2: Solve for x

Divide both sides of the equation \(6x = 18\) by 6.
\(x=\frac{18}{6}=3\)

Step3: Substitute x into one of the original equations

Substitute \(x = 3\) into the first equation \(3x+3y=15\).
We have \(3\times3+3y=15\), which simplifies to \(9 + 3y=15\).

Step4: Solve for y

Subtract 9 from both sides of the equation \(9+3y = 15\): \(3y=15 - 9=6\).
Then divide both sides by 3: \(y=\frac{6}{3}=2\)

Answer:

The solution of the system is \(x = 3,y = 2\) (or the ordered pair \((3,2)\))