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

Jul 8, 2016

The given pair of equations has no solution(s).

#### Explanation:

If
[1]$\textcolor{w h i t e}{\text{XXX}} y = 3 x + 4$
and
[2]$\textcolor{w h i t e}{\text{XXX}} y - 3 x = - 2$

Substituting (from [1]) $3 x + 4$ in place of $y$ into [2]
[3]$\textcolor{w h i t e}{\text{XXX}} \cancel{3 x} + 4 - \cancel{3 x} = - 2$

Since $4 \ne - 2$
these equations are inconsistent.

Jul 8, 2016

The system has no soln. , or, the Soln. Set $= \phi .$

#### Explanation:

Substituting the value of $y$, obtained from the first eqn., in the second eqn., we get,

$\left(3 x + 4\right) - 3 x = - 2 ,$ i.e., $4 = - 2$, which is an impossible result!

Hence, the Soln. Set $= \phi .$