[tex]\sf 5x+2y=21[/tex]
[tex]\sf -2x+6y=-34[/tex]
We could solve for 'x' in the 2nd equation and then plug that into the first equation for 'x' and solve for 'y':
[tex]\sf -2x+6y=-34[/tex]
Subtract 6y to both sides:
[tex]\sf -2x=-6y-34[/tex]
Divide -2 to both sides:
[tex]\sf x=3y+17[/tex]
Plug in 3y + 17 for 'x' in the first equation:
[tex]\sf 5x+2y=21[/tex]
[tex]\sf 5(3y+17)+2y=21[/tex]
Distribute 5:
[tex]\sf 15y+85+2y=21[/tex]
Combine like terms:
[tex]\sf 17y+85=21[/tex]
Subtract 85 to both sides:
[tex]\sf 17y=-64[/tex]
Divide 17 to both sides:
[tex]\boxed{\sf y\approx -3.8}[/tex]
This is the y-coordinate of the solution.
