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

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

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Answer 1 · 2015-10-29T10:20:40

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

Explanation:

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

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

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

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

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

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

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

Answer 2 · 2015-10-29T10:42:43

$x = \frac{13}{2}$ $x=13/2$
$y = \frac{- 11}{2}$ $y =(-11)/2$

Explanation:

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

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

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

$- 4 y = 22$ $-4y=22$
$y = \frac{22}{- 4} = \frac{- 22}{4} = \frac{- 11}{2}$ $y =22/(-4)=(-22)/4=(-11)/2$
$y = \frac{- 11}{2}$ $y =(-11)/2$

Substitute $y = \frac{- 11}{2}$ $y =(-11)/2$ in equation (1)

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

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

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