# How do solve the following linear system?:  4x+3y=1 , -6x-2y=-8 ?

the solution is:

$\left(x , y\right) \equiv \left(2.2 , - 2.6\right)$

#### Explanation:

$4 x + 3 y = 1$------(1)

$- 6 x - 2 y = - 8$------(2)

If
$a 11 x + a 12 y = b 11$
$a 21 x + a 22 y = b 21$

Then,

$x = \frac{b 11 a 22 - b 21 a 12}{a 11 a 22 - a 21 a 12}$

$y = \frac{a 11 b 21 - a 21 b 11}{a 11 a 22 - a 21 a 12}$

Here,

a11=4; a12=3; b11=1

a21=-6; a22=-2; b21=-8

Substituting

$x = \frac{1 \times \left(- 2\right) - \left(- 8\right) \times 3}{4 \times \left(- 2\right) - \left(- 6\right) \times 3} = \frac{- 2 + 24}{- 8 + 18} = \frac{22}{10} = 2.2$

$y = \frac{4 \times \left(- 8\right) - \left(- 6\right) \times 1}{4 \times \left(- 2\right) - \left(- 6\right) \times 3} = \frac{- 32 + 6}{- 8 + 18} = - \frac{26}{10} = - 2.6$

Check:

$l h s = 4 x + 3 y = 4 \times 2.2 + 3 \times \left(- 2.6\right) = 8.8 - 7.8 = 1 = r h s$

$l h s = - 6 x - 2 y = - 6 \times 2.2 - 2 \times \left(- 2.6\right) = - 13.2 + 5.2 = - 8 = r h s$

Hence,
the solution is:

$\left(x , y\right) \equiv \left(2.2 , - 2.6\right)$