Algebra II : Solving Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Linear Systems With Three Variables

Solve this system of equations.

Possible Answers:

, ,

, ,

, ,

, ,

, ,

Correct answer:

, ,

Explanation:

Equation 1:

Equation 2:

Equation 3:

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 #1 : Solving Equations

Solve for

Possible Answers:

Correct answer:

Explanation:

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 #2 : Solving Equations

Solve this system of equations for :

Possible Answers:

Correct answer:

Explanation:

Multiply the top equation by 3 on both sides, then add the second equation to eliminate the  terms:

 

 

Example Question #1 : Solving Equations

Solve for .

 

Possible Answers:

Correct answer:

Explanation:

 

Multiply both sides by 3:

 

 

Distribute:

Subtract  from both sides:

Add the  terms together, and subtract  from both sides:

Divide both sides by :

Simplify:

Example Question #2 : Solving Equations

Solve for :

Possible Answers:

Correct answer:

Explanation:

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 :.

 

Possible Answers:

Correct answer:

Explanation:

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 #28 : Solving Equations

Solve the system of equations.

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

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 #29 : Solving Equations

Solve for  and .

Possible Answers:

Cannot be determined.

Correct answer:

Explanation:

 

1st equation:

2nd equation:

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 #4 : Solving Equations

What is a solution to this system of equations:

Possible Answers:

Correct answer:

Explanation:

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 4: solve for z.
 
 
Step 5: solve for y.

Step 6: solve for x by substituting y=2 and z=1 into the first equation.

Example Question #3 : Solving Equations

What is a solution to this system of equations?

Possible Answers:

Correct answer:

Explanation:

Substitute equation 2. into equation 1.,

so, 

Substitute  into equation 2:

so, the solution is .

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