[tex]\huge\boxed{y=\frac{2}{5}x+2}\ \boxed{y=-\frac{1}{3}x+7}\ \boxed{y=2x-6}[/tex]
To solve each of these problems, we need to find [tex]y[/tex].
Problem 1
[tex]-2x+5y=10[/tex]
Add [tex]2x[/tex] to both sides of the equation. Our goal is to get [tex]y[/tex] by itself.
[tex]5y=2x+10[/tex]
Divide everything by [tex]5[/tex].
[tex]\boxed{y=\frac{2}{5}x+2}[/tex]
Problem 2
[tex]-x-3y=-21[/tex]
Add [tex]x[/tex] to both sides of the equation.
[tex]-3y=x-21[/tex]
Divide everything by [tex]-3[/tex].
[tex]\displaystyle y=-\frac{x}{3}+7[/tex]
Separate [tex]-\frac{x}{3}[/tex] into a coefficient and a variable.
[tex]\boxed{y=-\frac{1}{3}x+7}[/tex]
Problem 3
[tex]2y-4x=-12[/tex]
Add [tex]4x[/tex] to both sides of the equation.
[tex]2y=4x-12[/tex]
Divide everything by [tex]2[/tex].
[tex]\boxed{y=2x-6}[/tex]
