# How do solve the following linear system?:  4x+21y=6 , 4x-3y=1 ?

Mar 23, 2016

The solution for the system of equations is:
color(green)(x =13/32

color(green)(y=5/24

#### Explanation:

$\textcolor{b l u e}{4 x} + 21 y = 6$.........equation $\left(1\right)$
$\textcolor{b l u e}{4 x} - 3 y = 1$...........equation $\left(2\right)$

Solving by elimination:
Subtracting equation $2$ from $1$:

$\cancel{\textcolor{b l u e}{4 x}} + 21 y = 6$
$- \cancel{\textcolor{b l u e}{4 x}} + 3 y = - 1$

$24 y = 5$

color(green)(y=5/24

Finding $x$ from equation $1$:

$4 x + 21 y = 6$

$4 x = 6 - 21 y$

4x = 6 - 21 * color(green)(5/24

$4 x = 6 - \frac{105}{24}$

$4 x = \frac{144}{24} - \frac{105}{24}$

$4 x = \frac{39}{24}$

$x = \frac{39}{24 \cdot 4}$

color(green)(x =13/32