### All Algebra 1 Resources

## Example Questions

### Example Question #11 : Systems Of Equations

Solve the following equation for :

**Possible Answers:**

**Correct answer:**

The first step is to distribute (multiply) the 2 through the parentheses:

Then isolate on the left side of the equation. Subtract the 10 from the left and right side.

Finally, to isolate , divide the left side by 2 so that the 2 cancels out. Then divide by 2 on the right side as well.

You can verify this answer by plugging the into the original equation.

### Example Question #11 : How To Find The Solution To An Equation

Solve for :

**Possible Answers:**

None of the other answers

**Correct answer:**

To solve for , isolate it from the other variables. First, subtract from both sides to get

.

Then, divide both sides by to get

### Example Question #12 : Systems Of Equations

Solve for :

**Possible Answers:**

**Correct answer:**

To solve for , add to both sides to get

Then, multiply both sides by to get

### Example Question #13 : Systems Of Equations

Solve for :

**Possible Answers:**

**Correct answer:**

First, combine like terms within the equation to get

.

Then, add and subtract from both sides to get

.

Finally, divide both sides by to get the solution of .

### Example Question #13 : How To Find The Solution To An Equation

Solve for :

**Possible Answers:**

**Correct answer:**

First, use the distributive property to simplify the right side of the equation. This gives you

Then, subtract and add to both sides of the equation to get .

### Example Question #14 : Systems Of Equations

Solve for :

**Possible Answers:**

**Correct answer:**

First, use the distributive property to simplify the right side of the equation:

Then, add and subtract from both sides to get

Finally, divide both sides by to get .

### Example Question #15 : Systems Of Equations

Solve for , given the equation below.

**Possible Answers:**

No solutions

**Correct answer:**

Begin by cross-multiplying.

Distribute the on the left side and expand the polynomial on the right.

Combine like terms and rearrange to set the equation equal to zero.

Now we can isolate and solve for by adding to both sides.

### Example Question #16 : Systems Of Equations

Simplify the result of the following steps, to be completed in order:

1. Add to

2. Multiply the sum by

3. Add to the product

4. Subtract from the sum

**Possible Answers:**

**Correct answer:**

Step 1: 7*x* + 3*y*

Step 2: 4 * (7*x* + 3*y*) = 28*x* + 12*y*

Step 3: 28*x* + 12*y* + *x* = 29*x* + 12*y*

Step 4: 29*x* + 12*y* – (*x* – *y*) = 29*x* + 12*y* – *x* + *y* = 28*x* + 13*y*

### Example Question #17 : Systems Of Equations

What is ?

**Possible Answers:**

The answer cannot be determined.

**Correct answer:**

The key to solving this question is noticing that we can factor out a 2:

2*x* + 6*y* = 44 is the same as 2(*x* + 3*y*) = 44.

Therefore, *x* + 3*y* = 22.

In this case, *x* + 3*y* + 33 is the same as 22 + 33, or 55.

### Example Question #18 : Systems Of Equations

Solve for .

**Possible Answers:**

Cannot be determined

**Correct answer:**

Subtract x from both sides of the second equation.

Divide both sides by to get .

Plug in y to the other equation.

Divide 10 by 5 to eliminate the fraction, yielding .

Distribute the 2 to get .

Add to each side, and subtract 15 from each side to get .

Divide both sides by 7 to get , which simplifies to .

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