How do you solve $x + y = 1$ and $3x – y = 11$ using substitution?

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Answer 1 · 2016-05-10T12:17:09

The solution for the system of equations is:
$color(green)(x = 3$
$color(green)( y = -2$

$x + y = 1$
$color(blue)(x = 1 - y$ ........equation $(1)$

$3x - y =11$ ......equation $(2)$

Solving by substitution:

Substituting equation $1$ in $2$ :

$3x - y =11$

$3 * color(blue)((1 - y)) - y =11$

$3 -3 y - y =11$

$3 -4y =11$

$3 -11 = 4y$

$-8 = 4y$

$y = - 8 / 4$

$color(green)( y = -2$

Finding $x$ from equation $1:$

$color(blue)(x = 1 - y$

$x = 1 - (-2)$

$x = 1 + 2$

$color(green)(x = 3$

How do you solve x + y = 1x + y = 1 and 3x – y = 113x – y = 11 using substitution?