# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 8x-2y=6 and 3x+y=4?

Feb 9, 2016

Solution is $x = 1$ and $y = 1$

#### Explanation:

In these pair of linear equations, you can eliminate $x$ simply by doubling and then addting second equation to first, which gives

$\left(8 x - 2 y\right) + 2 \cdot \left(3 x + y\right) = 6 + 2 \cdot 4$ i.e.

$8 x + 6 x = 6 + 8$

or $14 x = 14$

or $x = 1$

Putting this in second equation $3 \cdot 1 + y = 4$ or

$3 + y = 4$ i.e. $y = 1$

Hence solution is $x = 1$ and $y = 1$