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Finite Math Examples
, ,
Step 1
Step 1.1
Add to both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
Step 2
Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
Step 2.2.1
Simplify .
Step 2.2.1.1
Simplify each term.
Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Simplify.
Step 2.2.1.1.2.1
Multiply by .
Step 2.2.1.1.2.2
Multiply by .
Step 2.2.1.2
Simplify by adding terms.
Step 2.2.1.2.1
Add and .
Step 2.2.1.2.2
Subtract from .
Step 3
Step 3.1
Move all terms not containing to the right side of the equation.
Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Add to both sides of the equation.
Step 3.1.3
Subtract from .
Step 3.2
Divide each term in by and simplify.
Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
Step 3.2.2.1
Cancel the common factor of .
Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.2.3
Simplify the right side.
Step 3.2.3.1
Move the negative in front of the fraction.
Step 4
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify .
Step 4.2.1
Simplify the left side.
Step 4.2.1.1
Remove parentheses.
Step 4.2.2
Simplify the right side.
Step 4.2.2.1
Simplify .
Step 4.2.2.1.1
Write as a fraction with a common denominator.
Step 4.2.2.1.2
Combine the numerators over the common denominator.
Step 4.2.2.1.3
Subtract from .
Step 4.2.2.1.4
Move the negative in front of the fraction.
Step 4.2.2.1.5
To write as a fraction with a common denominator, multiply by .
Step 4.2.2.1.6
Combine and .
Step 4.2.2.1.7
Combine the numerators over the common denominator.
Step 4.2.2.1.8
Combine the numerators over the common denominator.
Step 4.2.2.1.9
Multiply by .
Step 4.2.2.1.10
Subtract from .
Step 4.2.2.1.11
Rewrite as .
Step 4.2.2.1.12
Factor out of .
Step 4.2.2.1.13
Factor out of .
Step 4.2.2.1.14
Move the negative in front of the fraction.
Step 4.3
Replace all occurrences of in with .
Step 4.4
Simplify the left side.
Step 4.4.1
Simplify .
Step 4.4.1.1
Simplify each term.
Step 4.4.1.1.1
Apply the distributive property.
Step 4.4.1.1.2
Multiply .
Step 4.4.1.1.2.1
Multiply by .
Step 4.4.1.1.2.2
Combine and .
Step 4.4.1.1.2.3
Multiply by .
Step 4.4.1.1.3
Multiply .
Step 4.4.1.1.3.1
Combine and .
Step 4.4.1.1.3.2
Multiply by .
Step 4.4.1.1.4
Move the negative in front of the fraction.
Step 4.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.3
Combine and .
Step 4.4.1.4
Combine the numerators over the common denominator.
Step 4.4.1.5
Combine the numerators over the common denominator.
Step 4.4.1.6
Multiply by .
Step 4.4.1.7
Add and .
Step 4.4.1.8
Factor out of .
Step 4.4.1.8.1
Factor out of .
Step 4.4.1.8.2
Factor out of .
Step 4.4.1.8.3
Factor out of .
Step 4.4.1.9
Rewrite as .
Step 4.4.1.10
Factor out of .
Step 4.4.1.11
Factor out of .
Step 4.4.1.12
Move the negative in front of the fraction.
Step 5
Step 5.1
Multiply both sides of the equation by .
Step 5.2
Simplify both sides of the equation.
Step 5.2.1
Simplify the left side.
Step 5.2.1.1
Simplify .
Step 5.2.1.1.1
Cancel the common factor of .
Step 5.2.1.1.1.1
Move the leading negative in into the numerator.
Step 5.2.1.1.1.2
Move the leading negative in into the numerator.
Step 5.2.1.1.1.3
Factor out of .
Step 5.2.1.1.1.4
Cancel the common factor.
Step 5.2.1.1.1.5
Rewrite the expression.
Step 5.2.1.1.2
Cancel the common factor of .
Step 5.2.1.1.2.1
Factor out of .
Step 5.2.1.1.2.2
Cancel the common factor.
Step 5.2.1.1.2.3
Rewrite the expression.
Step 5.2.1.1.3
Multiply.
Step 5.2.1.1.3.1
Multiply by .
Step 5.2.1.1.3.2
Multiply by .
Step 5.2.2
Simplify the right side.
Step 5.2.2.1
Simplify .
Step 5.2.2.1.1
Multiply .
Step 5.2.2.1.1.1
Multiply by .
Step 5.2.2.1.1.2
Combine and .
Step 5.2.2.1.1.3
Multiply by .
Step 5.2.2.1.2
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
Subtract from 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
Subtract from .
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
Move the negative in front of the fraction.
Step 5.4.3.3
Multiply .
Step 5.4.3.3.1
Multiply by .
Step 5.4.3.3.2
Multiply by .
Step 5.4.3.3.3
Multiply by .
Step 5.4.3.3.4
Multiply by .
Step 6
Step 6.1
Replace all occurrences of in with .
Step 6.2
Simplify the right side.
Step 6.2.1
Simplify .
Step 6.2.1.1
Simplify the numerator.
Step 6.2.1.1.1
Cancel the common factor of .
Step 6.2.1.1.1.1
Factor out of .
Step 6.2.1.1.1.2
Factor out of .
Step 6.2.1.1.1.3
Cancel the common factor.
Step 6.2.1.1.1.4
Rewrite the expression.
Step 6.2.1.1.2
Combine and .
Step 6.2.1.1.3
Multiply by .
Step 6.2.1.1.4
Write as a fraction with a common denominator.
Step 6.2.1.1.5
Combine the numerators over the common denominator.
Step 6.2.1.1.6
Add and .
Step 6.2.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 6.2.1.3
Cancel the common factor of .
Step 6.2.1.3.1
Factor out of .
Step 6.2.1.3.2
Cancel the common factor.
Step 6.2.1.3.3
Rewrite the expression.
Step 6.3
Replace all occurrences of in with .
Step 6.4
Simplify the right side.
Step 6.4.1
Simplify .
Step 6.4.1.1
Combine the numerators over the common denominator.
Step 6.4.1.2
Multiply .
Step 6.4.1.2.1
Combine and .
Step 6.4.1.2.2
Multiply by .
Step 6.4.1.3
To write as a fraction with a common denominator, multiply by .
Step 6.4.1.4
Combine and .
Step 6.4.1.5
Combine the numerators over the common denominator.
Step 6.4.1.6
Simplify the numerator.
Step 6.4.1.6.1
Multiply by .
Step 6.4.1.6.2
Add and .
Step 6.4.1.7
Multiply the numerator by the reciprocal of the denominator.
Step 6.4.1.8
Cancel the common factor of .
Step 6.4.1.8.1
Factor out of .
Step 6.4.1.8.2
Cancel the common factor.
Step 6.4.1.8.3
Rewrite the expression.
Step 7
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 8
The result can be shown in multiple forms.
Point Form:
Equation Form: