Question

find the solution of the system of equations.

$-3x + 8y = -5$

$6x + 2y = -8$

Explanation:

Step1: Eliminate x by multiplying first equation

Multiply the first equation \(-3x + 8y = -5\) by 2 to get \(-6x + 16y = -10\).

Step2: Add the two equations

Add the new first equation \(-6x + 16y = -10\) and the second equation \(6x + 2y = -8\):
\((-6x + 6x)+(16y + 2y)=-10 + (-8)\)
\(18y=-18\)

Step3: Solve for y

Divide both sides by 18: \(y = \frac{-18}{18}=-1\)

Step4: Substitute y into second equation

Substitute \(y = -1\) into \(6x + 2y = -8\):
\(6x + 2(-1)=-8\)
\(6x - 2=-8\)

Step5: Solve for x

Add 2 to both sides: \(6x=-8 + 2=-6\)
Divide by 6: \(x=\frac{-6}{6}=-1\)

Answer:

The solution is \(x = -1\), \(y = -1\) (or as an ordered pair \((-1, -1)\))