Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you solve the system $x - 3 y = 3$ $x - 3y = 3$ and $2 x + 9 y = 11$ $2x + 9y = 11$ by substitution?

1 Answer

May 29, 2015

$[1] XXXXX x - 3 y = 3$ $[1]color(white)("XXXXX")x-3y = 3$
$[2] XXXXX 2 x + 9 y = 11$ $[2]color(white)("XXXXX")2x+9y = 11$

Rearrange [1] to get an expression for $x$ $x$
$[3] XXXXX x = 3 + 3 y$ $[3]color(white)("XXXXX")x=3+3y$

Substitute the expression for $x$ $x$ from [3] into [2]
$[4] XXXXX 2 (3 + 3 y) + 9 y = 11$ $[4]color(white)("XXXXX")2(3+3y)+9y = 11$

Simplify
$[5] XXXXX 6 + 6 y + 9 y = 11$ $[5]color(white)("XXXXX")6+6y+9y = 11$
$[6] XXXXX 15 y = 5$ $[6]color(white)("XXXXX")15y= 5$
$[7] XXXXX y = \frac{1}{3}$ $[7]color(white)("XXXXX")y=1/3$

Substitute the value of $y$ $y$ from [7] into [1]
$[8] XXXXX x - 3 (\frac{1}{3}) = 3$ $[8]color(white)("XXXXX")x-3(1/3) = 3$

Simplify
$[9] XXXXX x = 4$ $[9]color(white)("XXXXX")x=4$

The solution is $(x, y) = (4, \frac{1}{3})$ $(x,y) = (4,1/3)$

Related questions

See all questions in Linear Inequalities in Two Variables

Impact of this question

4863 views around the world

You can reuse this answer
Creative Commons License