EQUATION IN TWO VARIABLES:

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Presentation transcript:

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.

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.

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.

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

EXAMPLE LET X = -1 LET X = 0

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

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.

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