# Algebra 1 : Systems of Equations

## Example Questions

### Example Question #5 : Linear Equations

Solve for x:

Explanation:

Simplify the parenthesis:

Combine the terms with x's:

Combine constants:

### Example Question #31 : How To Find The Solution To An Equation

Solve for x:

None of these

Explanation:

Simplify the right side:

Isolate x:

Solve for

Explanation:

### Example Question #3 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

Explanation:

First. combine like terms to get

.

Then, add  and subtract from both sides to separate the terms.

This gives you .

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

### Example Question #1 : Solve Linear Equations With Rational Number Coefficients: Ccss.Math.Content.8.Ee.C.7b

Solve for :

Explanation:

First, you must multiply the left side of the equation using the distributive property.

This gives you .

Next, subtract  from both sides to get .

Then, divide both sides by  to get .

### Example Question #31 : Systems Of Equations

If , find the value of .

Explanation:

The simplest way to solve this is to test the answer choices provided by plugging them in the equation.  Start with the number in the middle, which in this case is 6. Replace every "B" in the equation with "6", and solve.

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Simplify the following:

Explanation:

Before you can add the two numerators from the fractions, the fractions must have a common denominator. The common denominator will be the Lowest Common Denominator (LCD). When you are dealing with variables, you get this by multiplying the two denominators together:

To follow through with this LCD, you must multiply each fraction by the other fraction's denominator so that they end up with common denominators. The first fraction needs to be multiplied by  and the second fraction needs to be multiplied by . Note that both of these are equivalent to ONE, so the value of the fraction does not change:

Now that the two fractions have common denominators, you can add the two numerators:

### Example Question #2 : How To Find The Solution To A Rational Equation With Lcd

Simplify the following:

Explanation:

Before you can subtract the two numerators from the fractions, the fractions must have a common denominator. The common denominator will be the Lowest Common Denominator (LCD). When you are dealing with variables, you get this by multiplying the two denominators together:

To follow through with this LCD, you must multiply each fraction by the other fraction's denominator so that they end up with common denominators. The first fraction needs to be multiplied by  and the second fraction needs to be multiplied by . Note that both of these are equivalent to ONE, so the value of the fraction does not change:

Now that the two fractions have common denominators, you can subtract the two numerators. You can also distribute the denominator so you can simplify later:

Finally you can divide out each term in the numerator and denominator by 2 to fully simplify the answer:

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Simplify:

Explanation:

Because the two rational expressions have the same denominator, we can simply add straight across the top.  The denominator stays the same.

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Solve for :

Explanation:

Multiply both sides by :

Factor this using the -method. We split the middle term using two integers whose sum is  and whose product is . These integers are :

Set each factor equal to 0 and solve separately:

or