Question

c. solve the system below using your method of choice.
2x + 3y = 18
4x - 3y = 6

Explanation:

Step1: Add the two equations

Adding \(2x + 3y=18\) and \(4x-3y = 6\) to eliminate \(y\).
\((2x + 3y)+(4x-3y)=18 + 6\)
\(2x+4x+3y - 3y=24\)
\(6x=24\)

Step2: Solve for \(x\)

Divide both sides of \(6x = 24\) by 6.
\(x=\frac{24}{6}=4\)

Step3: Substitute \(x = 4\) into the first - equation

Substitute \(x = 4\) into \(2x+3y = 18\).
\(2\times4+3y=18\)
\(8 + 3y=18\)

Step4: Solve for \(y\)

Subtract 8 from both sides: \(3y=18 - 8=10\), then \(y=\frac{10}{3}\)

Answer:

\(x = 4,y=\frac{10}{3}\)