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 \(y\):

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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 \(2x + 3y = 18\):

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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 \(y = 4\)