1. 2x + y = 18
2x - y = 22

2. 12a - 5b = 18
15a - 5b = 30

Solve by either the substitution or the addition-or-subtraction method.

3. 2m = n - 3
3m = 2n - 9

Can someone please explain to me what these methods are and how to use them? And what is the differnece between these?...Thanks for the help!

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3. Simultaneous equations?

2x + y = 18
2x - y = 22

Cancel out the x's by subtracting.

+ y = 18
- y = 22

Subtract these two lines.
y - (-y) = 2y
18 - 22 = -4

2y = -4
y = -2

Substitute y back into original equation.
2x + (-2) = 18
2x = 20
x = 10

x=10 y=-2

@qbkr21
I'll let you do the rest.

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#1

y=-2
x=10

5. Let's look at three examples using the "addition" or "subtraction" method for systems of equations:
1. Solve this system of equations
and check:
x - 2y = 14
x + 3y = 9
a. First, be sure that the variables are "lined up" under one another. In this problem, they are already "lined up".

x - 2y = 14
x + 3y = 9

b. Decide which variable ("x" or "y") will be easier to eliminate. In order to eliminate a variable, the numbers in front of them (the coefficients) must be the same or negatives of one another. Looks like "x" is the easier variable to eliminate in this problem since the x's already have the same coefficients.

x- 2y = 14
x+ 3y = 9

c.Now, in this problem we need to subtract to eliminate the "x" variable. Subtract ALL of the sets of lined up terms.
(Remember: when you subtract signed numbers, you change the signs and follow the rules for adding signed numbers.)

x - 2y = 14
-x - 3y = - 9

- 5y = 5

d. Solve this simple equation.
-5y = 5
y =
-1

e. Plug "y = -1" into either of the ORIGINAL equations to get the value for "x".
x - 2y = 14
x - 2(-1) = 14
x + 2 = 14
x =
12

f.Check:substitute x = 12 and y = -1 into BOTH ORIGINAL equations. If these answers are correct, BOTH equations will be TRUE!
x - 2y = 14
12
- 2(-1) = 14
12 + 2 = 14
14 = 14
(check!)

x + 3y = 9
12
+ 3(-1) = 9
12 - 3 = 9
9 = 9
(check!)

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7. Thanks a lot to all of you!