ACT Math : Algebra
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Example Questions
Example Question #27 : Systems Of Equations
Find a solution for the following system of equations:
x – y = 2
2x – 3y = 3
(3, 0)
(3, 1)
(1, 3)
(0, 0)
(0, 1)
(3, 1)
Use substitution and solve for one variable, then back substitute and solve for the other variable, or use elimination.
Example Question #241 : Equations / Inequalities
Solve the following system of equations:
There are two ways to solve this problem.
Option 1: The Substitution Method
Step 1: Set up the second equation so that 
Step 2: Substitute for 
Step 3: Plug 
Option 2: The Elimination Method
Step 1: Set up the equations so that the variables are on the same side
Step 2: Multiple the second equation by 2
Step 3: Subtract the second equation from the first (thereby canceling out the 
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Step 4: Substitute 
Example Question #2014 : Act Math
Solve for 
Setting both equations equal to 
and
Setting these expressions equal to each other gives
So, 
Plugging that back into the first equation:
The final answer is 
Example Question #1 : How To Find The Solution To An Inequality With Division
Solve for 
For the second equation, solve for 
Plug this value of y into the first equation.
Example Question #41 : How To Find The Solution For A System Of Equations
A store sells 17 coffee mugs for $169. Some of the mugs are $12 each and some are $7 each. How many $7 coffee mugs were sold?
9
7
8
6
10
7
The answer is 7.
Write two independent equations that represent the problem.
x + y = 17 and 12x + 7y = 169
If we solve the first equation for x, we get x = 17 – y and we can plug this into the second equation.
12(17 – y) + 7y = 169
204 – 12y + 7y =169
–5y = –35
y = 7
Example Question #45 : Systems Of Equations
What is the solution of 
We add the two systems of equations:
For the Left Hand Side:
For the Right Hand Side:
So our resulting equation is:
Divide both sides by 10:
For the Left Hand Side:
For the Right Hand Side:
Our result is:
Example Question #1 : Linear Equations With Whole Numbers
What is the solution of 
Reduce the second system by dividing by 3.
Second Equation:
Then we subtract the first equation from our new equation.
First Equation:
First Equation - Second Equation:
Left Hand Side:
Right Hand Side:
Our result is:
Example Question #32 : Basic Arithmetic
What is the solution of 
We first add both systems of equations.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
We divide both sides by 3.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
Example Question #3 : Creating Equations With Whole Numbers
What is the solution of 
We first multiply the second equation by 4.
So our resulting equation is:
Then we subtract the first equation from the second new equation.
Left Hand Side:
Right Hand Side:
Resulting Equation:
We divide both sides by -15
Left Hand Side:
Right Hand Side:
Our result is:
Example Question #2021 : Act Math
What is the value of 
When you have a set of two equations, you need to solve one for one of the variables. Then, you substitute that value into the other. For this set, we can even do something a little easier. Solve the second for 
Now,substitute into the first equation for 
Now, just simplify:
Now, use 
Finding the common denominator, you get:
Divide both sides by 
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