Question

3.
$2x + y = 3$
$2(-x + 3y = 12)$

Explanation:

Step1: Simplify the second equation

Multiply 2 into \(-x + 3y = 12\), we get \(-2x + 6y = 24\).

Step2: Add the two equations

Add \(2x + y = 3\) and \(-2x + 6y = 24\) together. The \(x\)-terms cancel: \((2x - 2x)+(y + 6y)=3 + 24\), so \(7y = 27\).

Step3: Solve for y

Divide both sides by 7: \(y=\frac{27}{7}\).

Step4: Substitute y into first equation

Plug \(y = \frac{27}{7}\) into \(2x + y = 3\): \(2x+\frac{27}{7}=3\). Subtract \(\frac{27}{7}\): \(2x=3-\frac{27}{7}=\frac{21 - 27}{7}=-\frac{6}{7}\).

Step5: Solve for x

Divide by 2: \(x=-\frac{3}{7}\).

Answer:

\(x = -\frac{3}{7}\), \(y=\frac{27}{7}\)