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

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)

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)