Question

1. x + 3y = 2

-x - 9y = -26

Explanation:

Step1: Add the two equations to eliminate \(x\)

The first equation is \(x + 3y = 2\) and the second is \(-x - 9y = -26\). Adding them together: \((x + 3y)+(-x - 9y)=2+(-26)\)
Simplify the left side: \(x - x + 3y - 9y=-6y\)
Simplify the right side: \(2 - 26=-24\)
So we have \(-6y=-24\)

Step2: Solve for \(y\)

Divide both sides of \(-6y = -24\) by \(-6\): \(y=\frac{-24}{-6}=4\)

Step3: Substitute \(y = 4\) into the first equation to find \(x\)

Substitute into \(x + 3y = 2\): \(x+3\times4 = 2\)
Simplify: \(x + 12 = 2\)
Subtract 12 from both sides: \(x=2 - 12=-10\)

Answer:

\(x=-10\), \(y = 4\)