# Algebra 1 : Systems of Equations

## Example Questions

### Example Question #11 : Systems Of Equations

Solve the following equation for :

Explanation:

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 :

Explanation:

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 :

Explanation:

To solve for , add  to both sides to get

Then, multiply both sides by  to get

### Example Question #13 : Systems Of Equations

Solve for :

Explanation:

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 :

Explanation:

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 :

Explanation:

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.

No solutions

Explanation:

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:

2. Multiply the sum by

4. Subtract from the sum

Explanation:

Step 1: 7x + 3y

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

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

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

### Example Question #17 : Systems Of Equations

What is ?

Explanation:

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

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

Therefore, x + 3y = 22.

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

### Example Question #18 : Systems Of Equations

Solve for .

Cannot be determined

Explanation:

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 .