Solving Systems of Equations by

You are given two equations:

y=2x+3

2y=x+6

You have to find one variable at a time, and it appears that it will be easier to find the value of x first.

First "y" in equation two with 2x+3.

2(2x+3)=x+6

Multiply 2x+3 by two and get

4x+6=x+6

Combine like terms on either sides and get

3x=0

so, x=0

In order to get the value of y, "x" in equation one with 0.

y=2(0)+3

Multiply the two and the zero

y=0+3

and zero plus three equals three.

Therefore, y=3.

The solution to the equations is written as

(0,3)

Another Example of

*****It is December and as a gift to yourself you are planning on buying 120 cans, about a year's worth, of surf wax. There are two kinds of surf wax that you favor. One is Roy Boy's, the cheaper of the two, that runs at $1 per can. The pricier wax, Aloha Bay, runs at $5 per can. With only $32 for 120 cans, how many of each brand of surf wax can you buy?

The first thing you must do is make two equations from the information given:

r + a = 120

1r + 5a = 32

Isolate one of the variables by subracting "a" from both sides. You will then get

r = -a + 120

Then the r in equation two with -a + 120 and get

(-a + 120) + 5a = 32

Combine like terms and get

4a = -88

a = -22

the "a" in equation one with -22

r - 22 = 120

r = 142

the solution is 142 cans of Roy Boy's and -22 cans of Aloha Bay ( it was stolen off of your porch that night)