ACT Math : Systems of Equations
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Example Questions
Example Question #243 : Equations / Inequalities
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 #1 : How To Evaluate Algebraic 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?
10
7
8
6
9
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 #31 : How To Find The Solution For A System 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 #2 : 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 #31 : 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 #521 : Algebra
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 #31 : Systems Of Equations
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 
Example Question #31 : Systems Of Equations
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. Either equation will work rather well, so use the first. Thus, from 
Now, substitute into the second equation:
Simplifying, you get:
Example Question #33 : Systems Of Equations
There are a variety of pitchers on a shelf, one that is blue and one that is red. For a given color, the amount of water held is the same. Three red and one blue pitcher hold 
Begin by writing out your data in equations. Based on the description, we know:
and ...
Now, to solve two equations like this, solve one equation for a variable. Then substitute into the other. The easiest one to solve is 
Now, substitute this into the other equation:
Simplify:
Luckily, this is just what we need!
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