How do you solve 5x - 1/2y = 24 and 3x - 2/3y = 41/3?

Aug 23, 2015

$\left\{\begin{matrix}x = 5 \\ y = 2\end{matrix}\right.$

Explanation:

You can solve this system of equations by multiplication.

Start by rewriting your two equations so that you can work without denominators.

$\left\{\begin{matrix}10 x - y = 48 \\ 9 x - 2 y = 41\end{matrix}\right.$

Notice that you can multiply the first equation by $- 2$ so that you get

$10 x - y = 48 | \cdot \left(- 2\right)$

$- 20 x + 2 y = - 96$

You can now add the two equations to cancel the $y$-terms and solve for $x$. Add the left side of the equations and the right side of the equations separately to get

$- 20 x + \textcolor{red}{\cancel{\textcolor{b l a c k}{2 y}}} + 9 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{2 y}}} = - 96 + 41$

$- 11 x = - 55 \implies x = \frac{\left(- 55\right)}{\left(- 11\right)} = \textcolor{g r e e n}{5}$

Use the value of $x$ in either one of the two equations to find the value of $y$

$10 \cdot 5 - y = 48$

$y = 50 - 48 = \textcolor{g r e e n}{2}$

The two solutions to this system of equations are

$\left\{\begin{matrix}x = 5 \\ y = 2\end{matrix}\right.$