All Algebra 1 Resources
Example Questions
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.
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 iscm.
We can then set each expression equal to.
The first expressioncan be solved by eitheror, but the other two expressions make it evident that the solution is.
Example Question #1 :How To Find The Solution For A System Of Equations
Solve the system forand.
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 multiplybyto get.
Then, we can addto this equation to yield, so.
We can plug that value into either of the original equations; for example,.
So,as well.
Example Question #1 :How To Find The Solution For A System Of Equations
What is the solution to the following system of equations:
By solving one equation for, and replacingin the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.
Example Question #2 :How To Find The Solution For A System Of Equations
Solve this system of equations for:
None of the other choices are correct.
Multiply the bottom equation by 5, then add to the top equation:
Example Question #3 :How To Find The Solution For A System Of Equations
Solve this system of equations for:
None of the other choices are correct.
Multiply the top equation by:
Now add:
Example Question #4 :How To Find The Solution For A System Of Equations
Solve this system of equations for:
None of the other choices are correct.
Multiply the top equation by:
Now add:
Example Question #3 :How To Find The Solution For A System Of Equations
Find the solution to the following system of equations.
To solve this system of equations, use substitution. First, convert the second equation to isolate.
Then, substituteinto the first equation for.
Combine terms and solve for.
Now that we know the value of, we can solve forusing our previous substitution equation.
Example Question #8 :How To Find The Solution For A System Of Equations
Find a solution for the following system of equations:
infinitely many solutions
no solution
no solution
When we add the two equations, theandvariables cancel leaving us with:
which means there is no solution for this system.
Example Question #9 :How To Find The Solution For A System Of Equations
Solve for:
None of the other answers
First, combine like terms to get. Then, subtract 12 andfrom both sides to separate the integers from the's to get. Finally, divide both sides by 3 to get.
Example Question #10 :How To Find The Solution For A System Of Equations
We have two linear functions:
Find the coordinate at which they intersect.
none of these
We are given the following system of equations:
We are to findand. We can solve this through the substitution method. First, substitute the second equation into the first equation to get
Solve forby adding 4x to both sides
Add 5 to both sides
Divide by 7
So. Use this value to findusing 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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