# How do you use substitution to determine if (0, 2) is an element of the solution set for the system of equations: x+3y=6, -x+4y=8?

Dec 14, 2016

$\text{ see explanation}$

#### Explanation:

Substitute the point (0 ,2). That is x = 0 , y = 2 into both equations and if they are TRUE then (0 ,2) is an element of the solution set.

$\text{ left side of 1st equation}$

$x + 3 y = 0 + \left(3 \times 2\right) = 6 = \text{ right side Hence TRUE}$

$\text{ left side of 2nd equation}$

$- x + 4 y = 0 + \left(4 \times 2\right) = 8 = \text{ right side Hence TRUE}$

Both equations are satisfied by (0 ,2) thus it is an element of the solution set.