# How do you find the inverse of 2x-3y= -15?

Apr 27, 2016

$\textcolor{b l u e}{\implies y = \frac{3}{2} x - \frac{15}{2}}$

#### Explanation:

Given:$\text{ } 2 x - 3 y = - 15$

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Note that the given equation $\to y = \frac{2}{3} x + 5$ ...............(1)
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Add $3 y$ to both sides

$2 x + 3 y - 3 y = - 15 + 3 y$

But $3 y - 3 y = 0$

$2 x = 3 y - 15$

Divide both sides by 2

$\frac{2}{2} \times x = \frac{3}{2} y - \frac{15}{2}$

But $\frac{2}{2} = 1$

$x = \frac{3}{2} y - \frac{15}{2}$ .....................(2)
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Where there is a $x$ in equation (2) write $y$
Where there is a $y$ in equation (2) write $x$

$\textcolor{b l u e}{\implies y = \frac{3}{2} x - \frac{15}{2}}$ .............................(3)
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$\textcolor{red}{\text{A inverse function is a reflection about } y = x}$