How do you solve the following system of equations?: 13x+3y=16, 17x-y=19?

Dec 22, 2015

The solution for the system of equations is:

color(blue)(x=73/64

color(blue)(y=25/64

Explanation:

$13 x + \textcolor{b l u e}{3 y} = 16$........equation $\left(1\right)$

$17 x - y = 19$, multiplying this equation by $3$
$51 x - \textcolor{b l u e}{3 y} = 57$..........equation $\left(2\right)$

Solving by elimination:

Adding equations $1$ and $2$

$13 x + \cancel{\textcolor{b l u e}{3 y}} = 16$

$51 x - \cancel{\textcolor{b l u e}{3 y}} = 57$

$64 x = 73$

color(blue)(x=73/64

Finding $y$ by substituting $x$ in equation $2$

$17 x - y = 19$

$17 x - 19 = y$

$17 \times \textcolor{b l u e}{\frac{73}{64}} - 19 = y$

$\left(\frac{1241}{64}\right) - \frac{19 \times 64}{64} = y$

$\left(\frac{1241}{64}\right) - \frac{1216}{64} = y$

$\left(\frac{25}{64}\right) = y$

color(blue)(y=25/64