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How do you solve the following system?: $2 x + y = 13, 3 x + 2 y = - 2$ $2x +y = 13 , 3x +2y = -2$

2 Answers

Jan 23, 2016

$(x, y) = (28, - 43)$ $(x,y)=(28,-43)$

Explanation:

Given:
[1] $XXX 2 x + y = 13$ $color(white)("XXX")2x+y=13$
[2] $XXX 3 x + 2 y = - 2$ $color(white)("XXX")3x+2y=-2$

Multiply [1] by $2$ $2$ to give $y$ $y$ a coefficient equal to that in [2]
[3] $XXX 4 x + 2 y = 26$ $color(white)("XXX")4x+2y=26$

Subtract [2] from [3] to eliminate the $y$ $y$ term
[4] $XXX x = 28$ $color(white)("XXX")x=28$

Substitute $28$ $28$ for $x$ $x$ back into [1]
[5] $XXX 2 \times 28 + y = 13$ $color(white)("XXX")2xx28 +y=13$

Simplify
[6] $XXX y = 13 - 56 = - 43$ $color(white)("XXX")y=13-56 = -43$

Jan 23, 2016

$x = 28$ $x=28$
$y = - 43$ $y=-43$

Explanation:

Given -

$2 x + y = 13$ $2x+y=13$ ---------------------------(1)
$3 x + 2 y = - 2$ $3x+2y=-2$ ---------------------------(2)

Solve equation (1) for $y$ $y$

$y = 13 - 2 x$ $y=13-2x$

Substitute $y = 13 - 2 x$ $y=13-2x$ in equation (2)

$3 x + 2 (13 - 2 x) = - 2$ $3x +2(13-2x)=-2$
$3 x + 26 - 4 x = - 2$ $3x+26-4x=-2$
$- x + 26 = - 2$ $-x+26=-2$
$- x = - 2 - 26$ $-x=-2-26$
$- x = - 28$ $-x=-28$
$x = 28$ $x=28$

Substitute $x = 28$ $x=28$ in equation (1)

$2 (28) + y = 13$ $2(28)+y=13$
$56 + y = 13$ $56+y=13$
$y = 13 - 56 = - 43$ $y=13-56=-43$
$y = - 43$ $y=-43$

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