How do you solve $y = -3x + 5$ and $5x - 4y = -3$ using substitution?

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Answer 1 · 2016-03-13T23:23:39

$x=1$
$y=2$

$1$ . Start by labelling the equations.

Equation $1$ : $color(orange)(y=-3x+5)$

Equation $2$ : $color(blue)(5x-4y=-3)$

$2$ . Substitute equation $1$ into equation $2$ .

$color(blue)(5x-4y=-3)$

$color(blue)(5x-4color(orange)((-3x+5))=-3)$

$3$ . Solve for $x$ .

$5x+12x-20=-3$

$17x=17$

$color(green)(|bar(ul(color(white)(a/a)x=1color(white)(a/a)|)))$

$4$ . Substitute $color(red)(x=1)$ into equation $1$ to find the value of $y$ .

$color(orange)(y=-3x+5)$

$color(orange)(y=-3color(red)((1))+5)$

$5$ . Solve.

$y=-3+5$

$color(green)(|bar(ul(color(white)(a/a)y=2color(white)(a/a)|)))$

$:.$ , $x$ is $1$ and $y$ is $2$ .

How do you solve y = -3x + 5 y = -3x + 5 and 5x - 4y = -35x - 4y = -3 using substitution?