Question

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`?

Answer 1

`" 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.

`" left side of 1st equation"`

`x+3y=0+(3xx2)=6=" right side Hence TRUE"`

`" left side of 2nd equation"`

`-x+4y=0+(4xx2)=8=" right side Hence TRUE"`

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