How do you solve x-2/3y=13 and 3/2x-y=17 using substitution?

Apr 23, 2016

These are equations of two straight lines. They are parallel so they do not share any points at all. Thus you can not equate one to the other. Hence there is no solution

Explanation:

$x - \frac{2}{3} y = 13$

$\frac{2}{3} y = x - 13$

$\textcolor{g r e e n}{y = \textcolor{red}{\frac{3}{2}} x - \frac{39}{2}}$...........................(1)
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$\frac{3}{2} x - y = 17$

$\textcolor{g r e e n}{y = \textcolor{red}{\frac{3}{2}} x - 17}$....................................(2)

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For standard form of $y = m x + c$ where $m \to$ gradient

$m = \frac{3}{2}$ in both casses