# Algebra Examples

,

Step 1

Multiply each equation by the value that makes the coefficients of opposite.

Step 2

Step 2.1

Simplify the left side.

Step 2.1.1

Simplify .

Step 2.1.1.1

Apply the distributive property.

Step 2.1.1.2

Multiply by .

Step 2.2

Simplify the right side.

Step 2.2.1

Multiply by .

Step 3

Add the two equations together to eliminate from the system.

Step 4

Step 4.1

Divide each term in by .

Step 4.2

Simplify the left side.

Step 4.2.1

Cancel the common factor of .

Step 4.2.1.1

Cancel the common factor.

Step 4.2.1.2

Divide by .

Step 4.3

Simplify the right side.

Step 4.3.1

Cancel the common factor of and .

Step 4.3.1.1

Factor out of .

Step 4.3.1.2

Cancel the common factors.

Step 4.3.1.2.1

Factor out of .

Step 4.3.1.2.2

Cancel the common factor.

Step 4.3.1.2.3

Rewrite the expression.

Step 5

Step 5.1

Substitute the value found for into one of the original equations to solve for .

Step 5.2

Simplify each term.

Step 5.2.1

Multiply .

Step 5.2.1.1

Combine and .

Step 5.2.1.2

Multiply by .

Step 5.2.2

Move the negative in front of the fraction.

Step 5.3

Move all terms not containing to the right side of the equation.

Step 5.3.1

Add to both sides of the equation.

Step 5.3.2

To write as a fraction with a common denominator, multiply by .

Step 5.3.3

Combine and .

Step 5.3.4

Combine the numerators over the common denominator.

Step 5.3.5

Simplify the numerator.

Step 5.3.5.1

Multiply by .

Step 5.3.5.2

Add and .

Step 5.3.6

Move the negative in front of the fraction.

Step 5.4

Divide each term in by and simplify.

Step 5.4.1

Divide each term in by .

Step 5.4.2

Simplify the left side.

Step 5.4.2.1

Cancel the common factor of .

Step 5.4.2.1.1

Cancel the common factor.

Step 5.4.2.1.2

Divide by .

Step 5.4.3

Simplify the right side.

Step 5.4.3.1

Multiply the numerator by the reciprocal of the denominator.

Step 5.4.3.2

Cancel the common factor of .

Step 5.4.3.2.1

Move the leading negative in into the numerator.

Step 5.4.3.2.2

Factor out of .

Step 5.4.3.2.3

Factor out of .

Step 5.4.3.2.4

Cancel the common factor.

Step 5.4.3.2.5

Rewrite the expression.

Step 5.4.3.3

Multiply by .

Step 5.4.3.4

Multiply by .

Step 5.4.3.5

Dividing two negative values results in a positive value.

Step 6

The solution to the independent system of equations can be represented as a point.

Step 7

The result can be shown in multiple forms.

Point Form:

Equation Form:

Step 8