How do solve the following linear system?:  5x-4y=23, 3x + 4y = -1 ?

Jan 13, 2016

The solution for system of equations is
color(blue)(x=11/4, y=-37/16

Explanation:

$5 x - \textcolor{b l u e}{4 y} = 23$ ......equation $\left(1\right)$

$3 x + \textcolor{b l u e}{4 y} = - 1$ ......equation $\left(2\right)$

Solving by elimination.

Adding equation $1$ and $2$

$5 x - \cancel{\textcolor{b l u e}{4 y}} = 23$

$3 x + \cancel{\textcolor{b l u e}{4 y}} = - 1$

$8 x = 22$

$x = \frac{22}{8}$

color(blue)(x=11/4

Finding $y$ from equation $1$

$5 x - 4 y = 23$

$5 x - 23 = 4 y$

$5 \times \frac{11}{4} - 23 = 4 y$

$\frac{55}{4} - 23 = 4 y$

$\frac{55}{4} - \frac{92}{4} = 4 y$

$- \frac{37}{4} = 4 y$

$- \frac{37}{4 \times 4} = y$

color(blue)(y=-37/16