How do you solve the system of equations x+ 3y = 8 and - x + 9y = 16?

1 Answer
May 10, 2017

See a solution process below:

Explanation:

Step 1) Solve the first equation for x:

x + 3y = 8

x + 3y - color(red)(3y) = 8 - color(red)(3y)

x + 0 = 8 - 3y

x = 8 - 3y

Step 2) Substitute 8 - 3y for x in the second equation and solve for y:

-x + 9y = 16 becomes:

-(8 - 3y) + 9y = 16

-8 + 3y + 9y = 16

-8 + (3 + 9)y = 16

-8 + 12y = 16

color(red)(8) - 8 + 12y = color(red)(8) + 16

0 + 12y = 24

12y = 24

(12y)/color(red)(12) = 24/color(red)(12)

(color(red)(cancel(color(black)(12)))y)/cancel(color(red)(12)) = 2

y = 2

Step 3) Substitute 2 for y into the solution for the first equation at the end of Step 1 and calculate x:

x = 8 - 3y becomes:

x = 8 - (3 * 2)

x = 8 - 6

x = 2

The solution is: x = 2 and y = 2 or (2, 2)