Question

2x + 3y = 18
2x - 3y = -6

Explanation:

Step1: Add the two equations

Adding the equations \(2x + 3y = 18\) and \(2x - 3y = -6\) to eliminate \(y\):
\[

$$\begin{align*} (2x + 3y)+(2x - 3y)&=18+(-6)\\ 2x + 3y+2x - 3y&=12\\ 4x&=12 \end{align*}$$

\]

Step2: Solve for \(x\)

Divide both sides of \(4x = 12\) by 4:
\[x=\frac{12}{4}=3\]

Step3: Substitute \(x = 3\) into one of the original equations

Substitute \(x = 3\) into \(2x + 3y = 18\):
\[

$$\begin{align*} 2\times3+3y&=18\\ 6 + 3y&=18 \end{align*}$$

\]

Step4: Solve for \(y\)

Subtract 6 from both sides: \(3y=18 - 6=12\)
Divide both sides by 3: \(y=\frac{12}{3}=4\)

Answer:

The solution to the system of equations is \(x = 3\) and \(y = 4\)