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Algebra 1 Help » Equations / Inequalities » Systems of Equations » Equations / Solution Sets » How to find the solution for a system of equations
Example Question #1 : How To Find The Solution For A System Of Equations
A cube has a volume of . If its width is, its length is, and its height is, find .
Possible Answers:
Correct answer:
Explanation:
Since the object in question is a cube, each of its sides must be the same length. Therefore, to get a volume of , each side must be equal to the cube root of , which is cm.
We can then set each expression equal to .
The first expression can be solved by either or , but the other two expressions make it evident that the solution is .
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Example Question #1 : How To Find The Solution For A System Of Equations
Solve the system for and .
Possible Answers:
Correct answer:
Explanation:
The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply by to get .
Then, we can add to this equation to yield , so .
We can plug that value into either of the original equations; for example, .
So, as well.
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Example Question #2 : How To Find The Solution For A System Of Equations
What is the solution to the following system of equations:
Possible Answers:
Correct answer:
Explanation:
By solving one equation for , and replacing in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.
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Example Question #1 : How To Find The Solution For A System Of Equations
Solve this system of equations for:
Possible Answers:
None of the other choices are correct.
Correct answer:
Explanation:
Multiply the bottom equation by 5, then add to the top equation:
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Example Question #2 : How To Find The Solution For A System Of Equations
Solve this system of equations for:
Possible Answers:
None of the other choices are correct.
Correct answer:
Explanation:
Multiply the top equation by:
Now add:
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Example Question #3 : How To Find The Solution For A System Of Equations
Solve this system of equations for :
Possible Answers:
None of the other choices are correct.
Correct answer:
Explanation:
Multiply the top equation by :
Now add:
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Example Question #4 : How To Find The Solution For A System Of Equations
Find the solution to the following system of equations.
Possible Answers:
Correct answer:
Explanation:
To solve this system of equations, use substitution. First, convert the second equation to isolate .
Then, substitute into the first equation for .
Combine terms and solve for .
Now that we know the value of , we can solve for using our previous substitution equation.
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Example Question #1 : How To Find The Solution For A System Of Equations
Find a solution for the following system of equations:
Possible Answers:
no solution
infinitely many solutions
Correct answer:
no solution
Explanation:
When we add the two equations, the and variables cancel leaving us with:
which means there is no solution for this system.
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Example Question #9 : How To Find The Solution For A System Of Equations
Solve for :
Possible Answers:
None of the other answers
Correct answer:
Explanation:
First, combine like terms to get . Then, subtract 12 and from both sides to separate the integers from the 's to get . Finally, divide both sides by 3 to get .
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Example Question #6 : How To Find The Solution For A System Of Equations
We have two linear functions:
Find the coordinate at which they intersect.
Possible Answers:
none of these
Correct answer:
Explanation:
We are given the following system of equations:
We are to find and . We can solve this through the substitution method. First, substitute the second equation into the first equation to get
Solve for by adding 4x to both sides
Add 5 to both sides
Divide by 7
So . Use this value to find using one of the equations from our given system of equations. I think I'll use the first equation (can also use the second equation).
So the two linear functions intersect at
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