# How to determine the number of solutions in a linear system without solving: y = 3x - 2 and 3x + y + 2 = 0 ?

Mar 15, 2016

1 solution

#### Explanation:

They are both straight line graphs.

The first has gradient of +3 and the second has gradient -3 so they cross. As they are straight lines they can only cross once.

They both have a constant that is the value of -2. Thus they cross at
$\left(x , y\right) \to \left(0 , - 2\right)$