# How do you find the ordered pair that is the solution of equations 5x - 4y + 3 = 15 and 9y = 4x + 31?

Jul 27, 2016

(x,y)=color(green)(""(8,7))

#### Explanation:

Rearrange the given equations into standard form:
[1]$\textcolor{w h i t e}{\text{XXX}} 5 x - 4 y = 12$
[2]$\textcolor{w h i t e}{\text{XXX}} 4 x - 9 y = - 31$

[1]$\times 4$ minus [2]$\times 5$
color(white)("XXXX")(20x-16y=color(white)("XXx")48)
$\textcolor{w h i t e}{\text{XXX}} \underline{- \left(20 x - 45 y = - 155\right)}$
$\textcolor{w h i t e}{\text{XXXXXXXXX")29y=color(white)("XX}} 203$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow y = \frac{203}{29} = 7$

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Similarly, [1]$\times 9$ minus [2]$\times 4$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = 8$