# Algebra II : Solving Equations

## Example Questions

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### Example Question #3 : How To Find A Solution Set

Solve this system of equations.

, ,

, ,

, ,

, ,

, ,

, ,

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 #5 : How To Find A Solution Set

Solve for

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 #1 : How To Subtract Trinomials

Solve this system of equations for :

Explanation:

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

### Example Question #5 : How To Factor A Variable

Solve for .

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 #4 : How To Find A Solution Set

Solve for :

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 #1 : Solving Equations

Solve for :.

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 #2 : Solving Equations

Solve the system of equations.

None of the other answers are correct.

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 #3 : Solving Equations

Solve for  and .

Cannot be determined.

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:

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 #1 : Solving Equations

What is a solution to this system of equations?

Explanation:

Substitute equation 2. into equation 1.,

so,

Substitute  into equation 2:

so, the solution is .

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