B.) y = 3.2x – 4

y = 3.1x – 3

The easiest way is to get both variables on one side.

3.2x – y = 4

3.1x – y = 3

Now, just subtract each term in the second equation from the corresponding term in the first.

3.2x – y = 4

3.1x – y = 3

—————-

0.1x + 0 = 1 (the y’s cancelled out)

0.1x = 1

x = 10

You then substitute the ten into either original equation to find ‘y.’ (3.1(10) – 3 = y, so 31 – 3 = y, so 28 = y).

See, you got the same answers (x = 10 and y = 28).

The answers are the same because both methods are meant to solve the system. The system’s answers are not going to change just because the method of solving changes (unless you do something wrong).

3.2x-4=3.1x-3

and you substituted y for Equation 1, and you just solve for x, and plug x back into either ORIGINAL equation to solve for y.

They are the same because they are linear.

Hope this helps.

…. y = 3.2x – 4

..- y = 3.1x – 3

——————–

..0y = .1x – 1

You basically subtract each of the values from the one above it. 3.2x – 3.1x = .1x and -4 – (-3) = -1

and 0y is just 0, I just put that into to show the result.

0 = .1x – 1

and when you solve for x, you get the same answer, which means it’s right.

The two methods agree with each other because it’s just two ways of elminating the ‘y’ variable from the equation. The method of subtracting one equation from the other just lets you do it all in one step instead of a series of steps which you did in the first method.

subtracting equations is like subtracting numbers. First, set up the equations like this:

y=3.1x-3

(-) y=3.2x-4

The minus sign in parenthesis is to signify that you are subtracting the equation. Now just subtract like you would say 6-2.

6

(-) 2

=

4

It is the same idea. y-y is equal to zero. then your equals sign, then 3.1x minus 3.2x, which is -.1x. finally -4 minus -3, which is -1. so you end up with the equation: 0=-.1x – 1. Now just solve for x.

KEEP IN MIND: you can only subtract like variables from each other to get a new number. for instance you can subtract y-5x, and you would still end up with y – 5x, but if you subtract 5x-3x you can get 2x.

Part b goes like this.

y = 3.2x -4

-(y = 3.1x -3)

——————

0=.1x -1

.1x=1

x=10

now you need to explain c. good luck,

ALi