How do you solve the following system using substitution?: $- 3 x + 3 y = 3, - 5 x + y = 13$ $-3x + 3y= 3, -5x + y = 13$

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Answer 1 · 2015-10-26T01:23:19

$x = - 3$ $x=-3$
$y = - 2$ $y=-2$

First, isolate $y$ $y$ in the first equation.

$[1] - 3 x + 3 y = 3$ $color(blue)([1])" "-3x+3y=3$

$[2] 3 y = 3 + 3 x$ $color(blue)([2])" "3y=3+3x$

$[3] y = 1 + x$ $color(blue)([3])" "y=1+x$

Now substitute the value of $y$ $y$ in the first equation to $y$ $y$ in the second equation.

$[1] - 5 x + y = 13$ $color(red)([1])" "-5x+color(blue)(y)=13$

$[2] - 5 x + (1 + x) = 13$ $color(red)([2])" "-5x+color(blue)((1+x))=13$

$[3] - 4 x = 12$ $color(red)([3])" "-4x=12$

$[4] x = - 3$ $color(red)([4])" "x=-3$

Now that we have the value of $x$ $x$ , we will simply substitute this to the first equation.

$[4] y = 1 + (- 3)$ $color(blue)([4])" "y=1+(-3)$

$[5] y = - 2$ $color(blue)([5])" "y=-2$

How do you solve the following system using substitution?: −3x+3y=3,−5x+y=13-3x + 3y= 3, -5x + y = 13