How do you solve $3x+y=16$ and $2x+y=11$ ?

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Answer 1 · 2015-06-30T03:59:25

The solutions are:
$color(blue)(x=5$
$color(blue)(y = 1$

$3x+color(green)(y)=16$ ........equation $(1)$

$2x+color(green)(y)=11$ ..........equation $(2)$

These equations can be solved through elimination :
(by eliminating $color(green)(y$ )

Subtracting equation $(2)$ from equation $(1)$ :

$3x+cancelcolor(green)(y)=16$

$-2x-cancelcolor(green)(y)=-11$

$color(blue)(x=5$

Now , finding $y$ , from equation $1$ :

$y = 16 -3x$
$= 16 - 3.(5)$
$color(blue)(y = 1$

How do you solve 3x+y=163x+y=16 and 2x+y=112x+y=11?