# What is the solution to the following system?: -6x + 10y = 5, -2x + 3y = -1

May 31, 2018

$x = \frac{25}{2}$

$y = 8$

#### Explanation:

Make $x$ or $y$ the subject and then substitute that in one of the equation.

$- 6 x + 10 y = 5$ -----> equation 1

$- 2 x + 3 y = - 1$ ------> equation 2

Lets make $x$ the subject in equation 1:

$- 6 x + 10 y = 5$

$- 6 x = 5 - 10 y$

$x = - \frac{5}{6} + \frac{10}{6} y$ ------> substitute $x$ in equation 2

$- 2 x + 3 y = - 1$ ------> equation 2

$- 2 \left(- \frac{5}{6} + \frac{10}{6} y\right) + 3 y = - 1$

$\frac{5}{3} - \frac{10}{3} y + 3 y = - 1$

$3 y - \frac{10}{3} y = - 1 - \frac{5}{3}$

$\frac{9 y - 10 y}{3} = \frac{- 3 - 5}{3}$

$- \frac{1}{3} y = - \frac{8}{3}$

$y = - \frac{8}{3} \times \left(- 3\right)$

$y = 8$

Substitute $y = 8$ in equation 2 to get value of $y$.

$- 2 x + 3 y = - 1$ ------> equation 2
$- 2 x + 3 \left(8\right) = - 1$

$- 2 x + 24 = - 1$

$- 2 x = - 1 - 24$

$- 2 x = - 25$

$x = \frac{25}{2}$

$- 6 x + 10 y = 5$ -----> equation 1
-6(25/2) + 10(8) = 5 -75+80 = 5# ----> correct