Finite Math Examples

Solve by Substitution 4x-3y=3 , -x-3y=3
,
Step 1
Solve for in .
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Step 1.1
Add to both sides of the equation.
Step 1.2
Divide each term in by and simplify.
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Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
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Step 1.2.2.1
Cancel the common factor of .
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Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 2
Replace all occurrences of with in each equation.
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Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.3
Combine and .
Step 2.2.1.4
Combine the numerators over the common denominator.
Step 2.2.1.5
Combine the numerators over the common denominator.
Step 2.2.1.6
Multiply by .
Step 2.2.1.7
Subtract from .
Step 2.2.1.8
Factor out of .
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Step 2.2.1.8.1
Factor out of .
Step 2.2.1.8.2
Factor out of .
Step 2.2.1.8.3
Factor out of .
Step 2.2.1.9
Rewrite as .
Step 2.2.1.10
Factor out of .
Step 2.2.1.11
Factor out of .
Step 2.2.1.12
Move the negative in front of the fraction.
Step 3
Solve for in .
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Step 3.1
Multiply both sides of the equation by .
Step 3.2
Simplify both sides of the equation.
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Step 3.2.1
Simplify the left side.
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Step 3.2.1.1
Simplify .
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Step 3.2.1.1.1
Cancel the common factor of .
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Step 3.2.1.1.1.1
Move the leading negative in into the numerator.
Step 3.2.1.1.1.2
Move the leading negative in into the numerator.
Step 3.2.1.1.1.3
Factor out of .
Step 3.2.1.1.1.4
Cancel the common factor.
Step 3.2.1.1.1.5
Rewrite the expression.
Step 3.2.1.1.2
Cancel the common factor of .
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Step 3.2.1.1.2.1
Factor out of .
Step 3.2.1.1.2.2
Cancel the common factor.
Step 3.2.1.1.2.3
Rewrite the expression.
Step 3.2.1.1.3
Multiply.
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Step 3.2.1.1.3.1
Multiply by .
Step 3.2.1.1.3.2
Multiply by .
Step 3.2.2
Simplify the right side.
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Step 3.2.2.1
Cancel the common factor of .
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Step 3.2.2.1.1
Move the leading negative in into the numerator.
Step 3.2.2.1.2
Cancel the common factor.
Step 3.2.2.1.3
Rewrite the expression.
Step 3.3
Move all terms not containing to the right side of the equation.
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Step 3.3.1
Subtract from both sides of the equation.
Step 3.3.2
Subtract from .
Step 3.4
Divide each term in by and simplify.
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Step 3.4.1
Divide each term in by .
Step 3.4.2
Simplify the left side.
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Step 3.4.2.1
Cancel the common factor of .
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Step 3.4.2.1.1
Cancel the common factor.
Step 3.4.2.1.2
Divide by .
Step 3.4.3
Simplify the right side.
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Step 3.4.3.1
Divide by .
Step 4
Replace all occurrences of with in each equation.
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Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the right side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Combine the numerators over the common denominator.
Step 4.2.1.2
Simplify the expression.
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Step 4.2.1.2.1
Multiply by .
Step 4.2.1.2.2
Subtract from .
Step 4.2.1.2.3
Divide by .
Step 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 6
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 7