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

Oct 29, 2015

$\left(x , y\right) = \left(6 \frac{13}{14} , - 5 \frac{1}{2}\right)$
$\textcolor{w h i t e}{\text{XXX}}$This may be wrong if I changed the first expression into the wrong equation, but it was meaningless as written

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXX")7x+5y=18color(white)("XXXXXX}}$note: I changed this from original version $7 x + 5 y + 18$
[2]$\textcolor{w h i t e}{\text{XXX}} - 7 x - 9 y = 4$

[3]$\textcolor{w h i t e}{\text{XXX}} - 4 y = 22$

Dividing both sides by $\left(- 4\right)$
[4]$\textcolor{w h i t e}{\text{XXX}} y = - 5 \frac{1}{2}$

Substituting $\left(- 5 \frac{1}{2}\right)$ for $y$ in [1]
[5]$\textcolor{w h i t e}{\text{XXX}} 7 x + 5 \left(- 5 \frac{1}{2}\right) = 18$

Simplifying
[6]$\textcolor{w h i t e}{\text{XXX}} 7 x - 27 \frac{1}{2} = 18$

[7]$\textcolor{w h i t e}{\text{XXX}} 7 x = 45 \frac{1}{2}$

[8]$\textcolor{w h i t e}{\text{XXX}} x = 6 \frac{13}{14}$

Oct 29, 2015

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

#### Explanation:

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

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

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

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

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

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