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Finite Math Examples
, ,
Step 1
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Add to 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 2.2.1.1.2.3
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 2.3
Replace all occurrences of in with .
Step 2.4
Simplify the left side.
Step 2.4.1
Simplify .
Step 2.4.1.1
Simplify each term.
Step 2.4.1.1.1
Rewrite as .
Step 2.4.1.1.2
Apply the distributive property.
Step 2.4.1.1.3
Simplify.
Step 2.4.1.1.3.1
Multiply by .
Step 2.4.1.1.3.2
Multiply by .
Step 2.4.1.1.3.3
Multiply by .
Step 2.4.1.2
Simplify by adding terms.
Step 2.4.1.2.1
Add and .
Step 2.4.1.2.2
Subtract from .
Step 3
Step 3.1
Move all terms not containing to the right side of the equation.
Step 3.1.1
Add to both sides of the equation.
Step 3.1.2
Subtract from 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
Divide by .
Step 4
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the left side.
Step 4.2.1
Simplify .
Step 4.2.1.1
Simplify each term.
Step 4.2.1.1.1
Apply the distributive property.
Step 4.2.1.1.2
Multiply .
Step 4.2.1.1.2.1
Combine and .
Step 4.2.1.1.2.2
Multiply by .
Step 4.2.1.1.3
Multiply by .
Step 4.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.3
Combine and .
Step 4.2.1.4
Combine the numerators over the common denominator.
Step 4.2.1.5
Find the common denominator.
Step 4.2.1.5.1
Write as a fraction with denominator .
Step 4.2.1.5.2
Multiply by .
Step 4.2.1.5.3
Multiply by .
Step 4.2.1.5.4
Write as a fraction with denominator .
Step 4.2.1.5.5
Multiply by .
Step 4.2.1.5.6
Multiply by .
Step 4.2.1.6
Combine the numerators over the common denominator.
Step 4.2.1.7
Simplify each term.
Step 4.2.1.7.1
Multiply by .
Step 4.2.1.7.2
Multiply by .
Step 4.2.1.7.3
Multiply by .
Step 4.2.1.8
Simplify by adding terms.
Step 4.2.1.8.1
Subtract from .
Step 4.2.1.8.2
Add and .
Step 4.3
Replace all occurrences of in with .
Step 4.4
Simplify the right 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
Combine and .
Step 4.4.1.1.2.2
Multiply by .
Step 4.4.1.1.3
Multiply by .
Step 4.4.1.1.4
Move the negative in front of the fraction.
Step 4.4.1.2
Add and .
Step 4.4.1.3
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.4
Simplify terms.
Step 4.4.1.4.1
Combine and .
Step 4.4.1.4.2
Combine the numerators over the common denominator.
Step 4.4.1.5
Simplify each term.
Step 4.4.1.5.1
Simplify the numerator.
Step 4.4.1.5.1.1
Factor out of .
Step 4.4.1.5.1.1.1
Factor out of .
Step 4.4.1.5.1.1.2
Factor out of .
Step 4.4.1.5.1.1.3
Factor out of .
Step 4.4.1.5.1.2
Multiply by .
Step 4.4.1.5.1.3
Add and .
Step 4.4.1.5.2
Multiply by .
Step 5
Step 5.1
Multiply both sides by .
Step 5.2
Simplify.
Step 5.2.1
Simplify the left side.
Step 5.2.1.1
Cancel the common factor of .
Step 5.2.1.1.1
Cancel the common factor.
Step 5.2.1.1.2
Rewrite the expression.
Step 5.2.2
Simplify the right side.
Step 5.2.2.1
Multiply by .
Step 5.3
Solve for .
Step 5.3.1
Move all terms not containing to the right side of the equation.
Step 5.3.1.1
Add to both sides of the equation.
Step 5.3.1.2
Add and .
Step 5.3.2
Divide each term in by and simplify.
Step 5.3.2.1
Divide each term in by .
Step 5.3.2.2
Simplify the left side.
Step 5.3.2.2.1
Cancel the common factor of .
Step 5.3.2.2.1.1
Cancel the common factor.
Step 5.3.2.2.1.2
Divide 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 each term.
Step 6.2.1.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 6.2.1.1.2
Cancel the common factor of .
Step 6.2.1.1.2.1
Factor out of .
Step 6.2.1.1.2.2
Cancel the common factor.
Step 6.2.1.1.2.3
Rewrite the expression.
Step 6.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 6.2.1.3
Combine and .
Step 6.2.1.4
Combine the numerators over the common denominator.
Step 6.2.1.5
Simplify the numerator.
Step 6.2.1.5.1
Multiply by .
Step 6.2.1.5.2
Add and .
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
Simplify each term.
Step 6.4.1.1.1
Combine and .
Step 6.4.1.1.2
Multiply by .
Step 6.4.1.1.3
Multiply the numerator by the reciprocal of the denominator.
Step 6.4.1.1.4
Cancel the common factor of .
Step 6.4.1.1.4.1
Factor out of .
Step 6.4.1.1.4.2
Cancel the common factor.
Step 6.4.1.1.4.3
Rewrite the expression.
Step 6.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 6.4.1.3
Combine and .
Step 6.4.1.4
Combine the numerators over the common denominator.
Step 6.4.1.5
Simplify the numerator.
Step 6.4.1.5.1
Multiply by .
Step 6.4.1.5.2
Subtract from .
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: