All Algebra II Resources
Example Question #1 : Linear Systems With Three Variables
Solve this system of equations.
Adding the terms of the first and second equations together will yield .
Then, add that to the third equation so that the y and z terms are eliminated. You will get .
This tells us that x = 1. Plug this x = 1 back into the systems of equations.
Now, we can do the rest of the problem by using the substitution method. We'll take the third equation and use it to solve for y.
Plug this y-equation into the first equation (or second equation; it doesn't matter) to solve for z.
We can use this z value to find y
So the solution set is x = 1, y = 2, and z = –5/3.
Example Question #4 : How To Find A Solution Set
Solve for :
To solve this problem we can first add to each side of the equation yielding
Then we take the square root of both sides to get
Then we calculate the square root of which is .
Example Question #1 : How To Subtract Trinomials
Solve this system of equations for :
Multiply the top equation by 3 on both sides, then add the second equation to eliminate the terms:
Example Question #2 : How To Factor A Variable
Solve for .
Multiply both sides by 3:
Subtract from both sides:
Add the terms together, and subtract from both sides:
Divide both sides by :
Example Question #1 : Solving Equations
Solve for :
Distribute the x through the parentheses:
x2 –2x = x2 – 8
Subtract x2 from both sides:
–2x = –8
Divide both sides by –2:
x = 4
Example Question #21 : How To Find The Solution To An Equation
Solve for :.
First factor the expression by pulling out :
Factor the expression in parentheses by recognizing that it is a difference of squares:
Set each term equal to 0 and solve for the x values:
Example Question #2 : Solving Equations
Solve the system of equations.
None of the other answers are correct.
Isolate in the first equation.
Plug into the second equation to solve for .
Plug into the first equation to solve for .
Now we have both the and values and can express them as a point: .
Example Question #3 : Solving Equations
Solve for and .
Cannot be determined.
Subtract the 2nd equation from the 1st equation to eliminate the "2y" from both equations and get an answer for x:
Plug the value of into either equation and solve for :
Example Question #2 : Linear Systems With Three Variables
What is a solution to this system of equations:
Step 1: Multiply first equation by −2 and add the result to the second equation. The result is:
Step 2: Multiply first equation by −3 and add the result to the third equation. The result is:
Step 3: Multiply second equation by −23 and add the result to the third equation. The result is:
Step 6: solve for x by substituting y=2 and z=1 into the first equation.
Example Question #4 : Solving Equations
What is a solution to this system of equations?
Substitute equation 2. into equation 1.,
Substitute into equation 2:
so, the solution is .