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What are x and y if $7x+5y=18$ and $-7x-9y=4$ ?

2 Answers

Oct 29, 2015

$(x,y) = (6 13/14, -5 1/2)$
$color(white)("XXX")$ This may be wrong if I changed the first expression into the wrong equation, but it was meaningless as written

Explanation:

[1] $color(white)("XXX")7x+5y=18color(white)("XXXXXX")$ note: I changed this from original version $7x+5y+18$
[2] $color(white)("XXX")-7x-9y=4$

Adding [1] and [2]
[3] $color(white)("XXX")-4y = 22$

Dividing both sides by $(-4)$
[4] $color(white)("XXX")y = -5 1/2$

Substituting $(-5 1/2)$ for $y$ in [1]
[5] $color(white)("XXX")7x+5(-5 1/2) =18$

Simplifying
[6] $color(white)("XXX")7x-27 1/2 = 18$

[7] $color(white)("XXX")7x = 45 1/2$

[8] $color(white)("XXX")x= 6 13/14$

Oct 29, 2015

$x=13/2$
$y =(-11)/2$

Explanation:

$7x+5y=18$ ----------------(1)
$-7x-9y=4$ -----------------(2)

Since the co-efficients of $x$ is $7$ and $-7$ , we can eliminate $x$ by adding the two equations.

$7x+5y=18$ ----------------(1) ADD with (2)
$-7x-9y=4$ -----------------(2)

$-4y=22$
$y =22/(-4)=(-22)/4=(-11)/2$
$y =(-11)/2$

Substitute $y =(-11)/2$ in equation (1)

$7x +5((-11)/2)=18$
$7x -55/2=18$ Multiply both sides by 2
$14x-55=36$
$14x=36+55$
$14x=91$
$x=91/14=13/2$
$x=13/2$

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