All Common Core: 8th Grade Math Resources
Example Questions
Example Question #1 : How To Find The Solution For A System Of Equations
Solve the system for and
.
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.
Example Question #201 : Grade 8
What is the solution to the following system of equations:
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.
Example Question #202 : Grade 8
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 #203 : Grade 8
Solve this system of equations for :
None of the other choices are correct.
Multiply the top equation by :
Now add:
Example Question #204 : Grade 8
Solve this system of equations for :
None of the other choices are correct.
Multiply the top equation by :
Now add:
Example Question #205 : Grade 8
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, 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.
Example Question #206 : Grade 8
Find a solution for the following system of equations:
no solution
infinitely many solutions
no solution
When we add the two equations, the and
variables cancel leaving us with:
which means there is no solution for this system.
Example Question #207 : Grade 8
Solve the set of equations:
Solve the first equation for :
Substitute into the second equation:
Multiply the entire equation by 2 to eliminate the fraction:
Using the value of , solve for
:
Therefore, the solution is
Example Question #208 : Grade 8
Solve the following system of equations:
Set the two equations equal to one another:
2x - 2 = 3x + 6
Solve for x:
x = -8
Plug this value of x into either equation to solve for y. We'll use the top equation, but either will work.
y = 2 * (-8) - 2
y = -18
Example Question #192 : Systems Of Equations
Solve this system of equations for :
None of the other choices are correct.
Multiply the bottom equation by , then add to the top equation:
Divide both sides by
All Common Core: 8th Grade Math Resources
