Question

solve each system by eli

1. ( x + 3y = 2 )

( -x - 9y = -26 )

Explanation:

Step1: Eliminate x by adding equations

Add the two equations \(x + 3y = 2\) and \(-x - 9y = -26\) 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 get \(-6y = -24\)

Step2: Solve for y

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

Step3: Substitute y into first equation

Substitute \(y = 4\) into \(x + 3y = 2\).
\(x + 3(4) = 2\)
Simplify: \(x + 12 = 2\)

Step4: Solve for x

Subtract 12 from both sides: \(x = 2 - 12 = -10\)

Answer:

The solution to the system is \(x = -10\), \(y = 4\)