How do you solve 3x + 3y = - 9; 6x + 2y = 23x+3y=9;6x+2y=2?

1 Answer
Jan 30, 2018

See a solution process below:

Explanation:

Step 1) Solve the first equation for xx:

3x +3y = -93x+3y=9

(3x +3y)/color(red)(3) = -9/color(red)(3)3x+3y3=93

(3x)/color(red)(3) +(3y)/color(red)(3) = -33x3+3y3=3

x + y = -3x+y=3

x + y - color(red)(y) = -3 - color(red)(y)x+yy=3y

x + 0 = -3 - yx+0=3y

x = -3 - yx=3y

Step 2) Substitute (-3 - y)(3y) for xx in the second equation and solve for yy:

6x + 2y = 26x+2y=2 becomes:

6(-3 - y) + 2y = 26(3y)+2y=2

(6 xx -3) - (6 xx y) + 2y = 2(6×3)(6×y)+2y=2

-18 - 6y + 2y = 2186y+2y=2

-18 + (-6 + 2)y = 218+(6+2)y=2

-18 + (-4)y = 218+(4)y=2

-18 - 4y = 2184y=2

-18 + color(red)(18) - 4y = 2 + color(red)(18)18+184y=2+18

0 - 4y = 2004y=20

-4y = 204y=20

(-4y)/color(red)(-4) = 20/color(red)(-4)4y4=204

(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = -5

y = -5

Step 3) Substitute -5 for y in the solution to the first equation at the end of Step 1 and calculate x:

x = -3 - y becomes:

x = -3 - (-5)

x = -3 + 5

x = 2

The Solution Is:

x = 2 and y = -5

Or

(2, -5)