How do you solve the system of equations: 2x + 3y = 6, x + y = 4?

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Answer 1 · 2015-08-08T06:39:08

The solution for the system of equations is
$color(blue)(x=6, y=-2$

$color(blue)(2x)+3y=6$ ......equation $(1)$

$x+y=4$ , multiplying this equation by $2$
$color(blue)(2x)+2y=8$ .....equation $(2)$

Solving by elimination , subtracting equation $2$ from $1$ results in elimination of $color(blue)(2x$

$cancelcolor(blue)(2x)+3y=6$
$-cancelcolor(blue)(2x)-2y=-8$

$color(blue)(y=-2$

Substituting the value of $y$ in equation $2$ to find $x$
$x+y=4$

$x=4-y$

$x=4-(-2)$

$color(blue)(x=6$