ACT Math : Equations / Inequalities
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Example Questions
Example Question #241 : Equations / Inequalities
Solve 
Adding the two equations together gives 
The sum of 
Example Question #26 : How To Find The Solution For A System Of Equations
Suppose x2 + x – 6 = 0. Which of the following could be a value of x?
0
3
1
4
2
2
Factor out this binomial. –3 and 2 are the only possible x values. 2 is the answer.
Example Question #27 : How To Find The Solution For A System Of Equations
Find a solution for the following system of equations:
x – y = 2
2x – 3y = 3
(3, 1)
(0, 0)
(0, 1)
(3, 0)
(1, 3)
(3, 1)
Use substitution and solve for one variable, then back substitute and solve for the other variable, or use elimination.
Example Question #25 : How To Find The Solution For A System Of Equations
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 #31 : Systems Of Equations
Solve for 
For the second equation, solve for 
Plug this value of y into the first equation.
Example Question #1 : Evaluating Expressions
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
6
7
10
8
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 #32 : Equations / Inequalities
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 #33 : 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 #34 : Whole Numbers
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:
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