# How do you solve 8y-1=x, 3x=2y?

Nov 26, 2016

I found: $x = \frac{1}{11} \mathmr{and} y = \frac{3}{22}$

#### Explanation:

We can trysubstituting the first equation, for $x$, intothe second to get:
$3 \cdot \left(\textcolor{red}{8 y - 1}\right) = 2 y$
Solve for $y$:
$24 y - 3 = 2 y$
$22 y = 3$
So: $y = \frac{3}{22}$
Using this value back into the first equation:
$8 \cdot \left(\frac{3}{22}\right) - 1 = x$
$x = \frac{24 - 22}{22} = \frac{2}{22} = \frac{1}{11}$

$\left(x , y\right) = \left(\frac{1}{11} , \frac{3}{22}\right)$

#### Explanation:

We have two equations:

$8 y - 1 = x$
$3 x = 2 y$

We can substitute in the value of x (in terms of y) from the first equation into the second, and then solve for y. Like this:

$3 \left(8 y - 1\right) = 2 y$

$24 y - 3 = 2 y$

$22 y = 3$

$y = \frac{3}{22}$

And then we substitute into either of the initial equations (I'll do both to show we'll get the same answer for x):

$8 y - 1 = x$

$8 \left(\frac{3}{22}\right) - 1 \left(1\right) = x$

$\frac{24}{22} - 1 \left(\frac{22}{22}\right) = x$

$\frac{24}{22} - \frac{22}{22} = \frac{2}{22} = \frac{1}{11} = x$

or:

$3 x = 2 y$

$3 x = 2 \left(\frac{3}{22}\right)$

$3 x = \frac{3}{11}$

$x = \frac{1}{11}$