# How do you solve the system 2x - 3y = 2-x and 3x - 2y = -2 + y?

Jul 12, 2016

The soln. does not exist, or, the Soln. Set is $\phi$.

#### Explanation:

Given eqns. are $: 2 x - 3 y = 2 - x \Rightarrow 2 x + x - 3 y = 2 \Rightarrow 3 x - 3 y = 2. \ldots \ldots . . \left(i\right)$

Similarly, from the second eqn., we have, $3 x - 3 y = - 2. \ldots \ldots \ldots \left(i i\right)$

Substituting the value of $3 x - 3 y$ from $\left(i\right)$ into $\left(i i\right)$, we see that,

$2 = - 2$, which is an impossible result.

Hence, the soln. does not exist, or, we can say that the Soln. Set is $\phi$.