1. EQUATION IN TWO VARIABLES:
EXAMPLE :
4X + 2Y = 10
A SOLUTION OF AN EQUATION IN TWO VARIABLES IS AN ORDERED PAIR, (X,Y).
AN EQUATION IN TWO VARIABLES WILL HAVE MANY ORDERED PAIRS THAT ARE SOLUTIONS.

2. REPLACEMENT SET DEFINITION:
SET OF VALUES USED TO REPLACE ONE OF THE VARIABLES IN AN EQUATION WITH 2 VARIABLES.
THIS ALLOWS YOU TO FIND THE VALUE OF THE OTHER VARIABLE.

3. TO FIND THE SOLUTIONS:
SOLVE THE EQUATION FOR Y, WHICH MEANS TO GET RID OF EVERYTHING ON THE SAME SIDE AS Y.
IF GIVEN A DOMAIN, REPLACE X WITH THESE VALUES AND FIND THE Y VALUES.

4. EXAMPLE SOLVE 4X + 2Y = 10 IF THE DOMAIN IS {-1, 0, 2, 4}.
1.SOLVE FOR Y

5. EXAMPLE
LET X = LET X = 0

6. EXAMPLE CONTINUED
LET X = 2 LET X = 4
THEREFORE THE SOLUTION SET IS:

7. TO DETERMINE IF AN ORDERED PAIR IS A SOLUTION TO AN EQUATION IN TWO VARIABLES:
REPLACE THE ORDERED PAIR INTO THE EQUATION.
IF THE STATEMENT IS TRUE THE ORDERED PAIR IS A SOLUTION, IF FALSE IT IS NOT.

8. EXAMPLE
IS (2,3) A SOLUTION TO THE EQUATION 2X + Y = 7?