# `1/3 x + y = 9` `-2x + 2y = -6` Solve the system using any algebraic method.

Asked on by nick-teal

### Textbook Question

Chapter 3, 3.2 - Problem 49 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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Educator Approved

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`x/3 + y = 9 and -2x + 2y = -6`

In `-2x + 2y = -6 ` move the 2y by adding it:

`-2x = -6 - 2y`

divide by -2 because we are trying to get x alone:

x = 3 + y

Now plug in this number as y in the other equation:

`(3+y)/3 + y = 9`

`y/3 + 1 + y = 9`

`(4y)/3 = 8`

y = 6

now plug this in into any of the other problems to solve for x:

x = 3 + 6

x = 9

Educator Approved

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The system of equations x/3 + y = 9 and -2x + 2y = -6 has to be solved.

Take -2x + 2y = -6

Divide both sides by -2

x - y = 3

x = y + 3

Substitute this in x/3 + y = 9

(y+3)/3 + y = 9

y/3 + 1 + y = 9

(4y)/3 = 8

y = 6

x = 9

The solution of the system of equations is x = 9, y = 6

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