Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth. 5x+2y=21-2x+6y=-34

[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.