[tex] -3x-8y=20\\ \\ -5x+y=19[/tex]
First let's multiply the first equation by -5 and the second one by 3
[tex]-5\cdot (-3x-8y)=-5\cdot 20\\ \\ 15x+40y=-100 [/tex]
[tex]3\cdot (-5x+y)=3\cdot 19\\ \\ -15x+3y=57\\ [/tex]
And now let's add these two new equations.
[tex]15x+40y=-100\\ \\ -15x+3y=57\\ \\ (15x+40y)+(-15x+3y)=-100+57\\ \\ 15x-15x+40y+3y=-43\\ \\ 43y=-43\\ \\ y=\quad \frac { 43 }{ -43 } \\ \\ y=\quad -1 [/tex]
We found y's value. Let's put it in one of the equations to find x.
[tex]y=\quad -1\\ \\ -3x-8y=20\\ \\ -3x-8\cdot -1=20\\ \\ -3x+8=20\\ \\ -3x=20-8\\ \\ -3x=12\\ \\ x=\quad \frac { 12 }{ -3 } \\ \\ x=-4 [/tex]
Solution : (-4, -1)
Good Luck !
