Question

find the solution of the system of equations.

$-x + 4y = 29$

$6x + 2y = -18$

Explanation:

Step1: Simplify the second equation

Divide the second equation \(6x + 2y=-18\) by 2, we get \(3x + y=-9\), then express \(y\) in terms of \(x\): \(y=-9 - 3x\).

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

Substitute \(y = -9 - 3x\) into \(-x + 4y=29\), we have \(-x+4(-9 - 3x)=29\).
Expand the left - hand side: \(-x-36 - 12x=29\).
Combine like terms: \(-13x-36 = 29\).
Add 36 to both sides: \(-13x=29 + 36=65\).
Divide both sides by - 13: \(x=\frac{65}{-13}=-5\).

Step3: Find the value of \(y\)

Substitute \(x = - 5\) into \(y=-9 - 3x\), we get \(y=-9-3\times(-5)=-9 + 15 = 6\).

Answer:

The solution of the system of equations is \(x=-5,y = 6\) (or in ordered pair form \((-5,6)\))