[tex]\sf -2x-5y=3[/tex]
[tex]\sf 3x+8y=-6[/tex]
Let's solve the second equation for 'x':
[tex]\sf 3x+8y=-6[/tex]
Subtract 8y to both sides:
[tex]\sf 3x=-8y-6[/tex]
Divide 3 to both sides:
[tex]\sf x=-\dfrac{8}{3}y-2[/tex]
Now let's plug this in for 'x' in the first equation:
[tex]\sf -2x-5y=3[/tex]
[tex]\sf -2(-\dfrac{8}{3}y-2)-5y=3[/tex]
Distribute:
[tex]\sf \dfrac{16}{3}y+4-5y=3[/tex]
Combine like terms:
[tex]\sf \dfrac{1}{3}y+4=3[/tex]
Subtract 4 to both sides:
[tex]\sf \dfrac{1}{3}y=-1[/tex]
Divide 1/3 to both sides or multiply by its reciprocal, 3:
[tex]\sf y=-3[/tex]
This is the y-value of our solution, we can plug it into any of the two equations to find the x-value:
[tex]\sf 3x+8y=-6[/tex]
[tex]\sf 3x+8(-3)=-6[/tex]
Multiply:
[tex]\sf 3x-24=-6[/tex]
Add 24 to both sides:
[tex]\sf 3x=18[/tex]
Divide 3 to both sides:
[tex]\sf x=6[/tex]
So our final solution is:
[tex]\boxed{\sf (6,-3)}[/tex]
