Question

of the system of equations.

$-x + 9y = -19$

$3x - 3y = 9$

Explanation:

Step1: Simplify the second equation

Divide the second equation \(3x - 3y = 9\) by 3, we get \(x - y = 3\), then express \(x\) as \(x = y + 3\).

Step2: Substitute \(x\) into the first equation

Substitute \(x = y + 3\) into \(-x + 9y = -19\), we have \(-(y + 3) + 9y = -19\).
Expand it: \(-y - 3 + 9y = -19\).
Combine like terms: \(8y - 3 = -19\).
Add 3 to both sides: \(8y = -16\).
Divide by 8: \(y = -2\).

Step3: Find \(x\) using \(x = y + 3\)

Substitute \(y = -2\) into \(x = y + 3\), we get \(x = -2 + 3 = 1\).

Answer:

The solution of the system is \(x = 1\), \(y = -2\)