Answer:
[tex]x=3\\y=-10[/tex]
Step-by-step explanation:
[tex]13x=-21-6y\\-8x=36+6y[/tex]
Let's take one of the equations and solve for x. I'll take the first one.
[tex]13x=-21-6y[/tex]
Divide by 13.
[tex]x=\frac{-21-6y}{13}[/tex]
Now replace x in the second equation.
[tex]-8x=36+6y\\-8(\frac{-21-6y}{13} )=36+6y[/tex]
Distribute -8
[tex]\frac{168+48y}{13}=36+6y[/tex]
Break down the fraction.
[tex]\frac{168}{13}+\frac{48}{13}y=36+6y[/tex]
Subtract [tex]\frac{168}{13}[/tex]
[tex]\frac{48}{13}y=36+6y-\frac{168}{13}[/tex]
Subtract 6y
[tex]\frac{48}{13}y-6y=36-\frac{168}{13}[/tex]
Combine like terms;
[tex]\frac{48-13*6}{13}y=\frac{36*13-168}{13}[/tex]
Solve;
[tex]\frac{48-78}{13}y=\frac{468-168}{13}[/tex]
Keep solving;
[tex]\frac{-30}{13}y=\frac{300}{13}[/tex]
Multiply by the negative reciprocal of the fraction next to y.
[tex](-\frac{13}{30} )\frac{-30}{13}y=\frac{300}{13}(-\frac{13}{30} )[/tex]
On the right side; 13 and 13 become 1. 300/30 = 30/3 = 10
[tex]y=-10[/tex]
After having found y, replace it in any of the equations to find x.
[tex]13x=-21-6y\\13x=-21-6(-10)\\13x=-21+60\\13x=39\\x=\frac{39}{13}\\ x=3[/tex]
