Solving system of equations y=3x+7 , y=-4x+21

Since both equations are set equal to y, you can set the equations equal to each other and solve for x.
3x + 7 = -4x + 21
Add 4x to both sides
7x + 7 = 21
Subtract 7 from both sides
7x = 14
Divide both sides by 7
x = 2
Now plug 2 back in either equation and solve for y.
y = 3(2) + 7
y = 13
(2,13)

The technique you would use for this is substitution since both equations are in y=mx+b form. 
3x+7=-4x+21
now solve.
subtract 4 on both sides
7x+7=21
then subtract 7 on both sides.
7x=14
then divide 7 on both sides
x=2
now, solve for y by plugging in to the first equation:
y=3x+7
y=3(2)+7
y=13
The solution set is (2,13)
to check if this is correct you plug in x and y to the second equation
y=-4x+21
13=-4(2)=21
13=13
The solution set is (2,13)