Question 222992: I was asked to solve the systems of linear equations by using the subtraction method... ok Im lost on these!
1.) x=y-2
x+3y=2
2.) x=4y-3
2x-3y=0
3.) y= 2x-9
3x-y=2
4.) 3x+4y=7
x=3-2y
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Since all these systems are ideally set up for the Substitution Method and since I've not heard of a "Subtraction" method, I'm going to assume that we're supposed to use the Substitution Method. If there really is a "Subtraction" method, then the following will not be illustrate the correct method. (The answers of course are the same no matter which method is used.)
The Substitution Method- Solve either equation for either of the variables.
- Substitute for that variable into the other equation. This creates a one-variable equation.
- Solve the one-variable equation
- Substitute the value of the "solved for" variable back into one of the original equations. This will create another one-variable equation.
- Solve this (second) one-variable equation.
Now let's try this out on your systems. Every system you have already has a variable "solved for". This measn we get to skip step 1 on each system.
(Remember that solving for a variable means getting that variable by itself on one side of the equation.) Each of your systems has an equation where one of the variables is already by itself (i.e. "solved for"). This is why I am assuming the Substitution Method.)
x=y-2
x+3y=2
Step 1: Solve an equation for one of the variables: In the first equation "x" is "solved for".
Step 2: Substitute into the other equation:
(y-2) + 3y = 2
Step 3: Solve this equation:
Simplify
4y - 2 = 2
4y = 4
y = 1
Step 4: Substitute this value into one of the original equations:
x = (1)-2
Step 5: Solve this equation:
x = -1
Solution: (-1, 1)
x=4y-3
2x-3y=0
Step 1: Solve an equation for one of the variables: In the first equation "x" is "solved for".
Step 2: Substitute into the other equation:
2(4y-3) - 3y = 0
Step 3: Solve this equation:
Simplify
8y - 6 - 3y = 0
5y - 6 = 0
5y = 6
y = 6/5
Step 4: Substitute this value into one of the original equations:
x = 4(6/5) - 3
Step 5: Solve this equation:
x = 24/5 - 3
x = 24/5 - 15/5
x = 9/5
Solution: (9/5, 6/5)
y = 2x-9
3x-y=2
Step 1: Solve an equation for one of the variables: In the first equation "y" is "solved for".
Step 2: Substitute into the other equation:
3x - (2x-9) = 2
(Note the parentheses! These are critical here and so it is a good idea to get in the habit of ALWAYS using parentheses when you substitute for a variable.)
Step 3: Solve this equation:
Simplify
3x - 2x + 9 = 2
x + 9 = 2
x = -7
Step 4: Substitute this value into one of the original equations:
y = 2(-7)-9
Step 5: Solve this equation:
y = -14-9
y = -23
Solution: (-7, -23)
3x+4y=7
x=3-2y
Step 1: Solve an equation for one of the variables: In the second equation "x" is "solved for".
Step 2: Substitute into the other equation:
3(3-2y) + 4y = 7
Step 3: Solve this equation:
Simplify
9 - 6y + 4y = 7
9 - 2y = 7
-2y = -2
y = 1
Step 4: Substitute this value into one of the original equations:
x = 3-2(1)
Step 5: Solve this equation:
x = 3-2
x = 1
Solution: (1, 1)
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