Finite Math Examples

Solve by Substitution -4x-8y-2z-6w=-5 , 4y+24z+8w=32 , 5z+5w=10 , -4w=-12
, , ,
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 1.3
Simplify the right side.
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Step 1.3.1
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
Multiply by .
Step 2.3
Replace all occurrences of in with .
Step 2.4
Simplify the left side.
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Step 2.4.1
Multiply by .
Step 2.5
Replace all occurrences of in with .
Step 2.6
Simplify the left side.
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Step 2.6.1
Multiply by .
Step 3
Solve for in .
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Step 3.1
Move all terms not containing to the right side of the equation.
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Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Subtract from .
Step 3.2
Divide each term in by and simplify.
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Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left 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
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.2.3
Simplify the right side.
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Step 3.2.3.1
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 left side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Multiply by .
Step 4.2.1.2
Combine the opposite terms in .
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Step 4.2.1.2.1
Add and .
Step 4.2.1.2.2
Add and .
Step 4.3
Replace all occurrences of in with .
Step 4.4
Simplify the left side.
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Step 4.4.1
Simplify .
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Step 4.4.1.1
Multiply by .
Step 4.4.1.2
Subtract from .
Step 5
Divide each term in by and simplify.
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Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
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Step 5.2.1
Cancel the common factor of .
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Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Divide by .
Step 5.3
Simplify the right side.
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Step 5.3.1
Divide by .
Step 6
Replace all occurrences of with in each equation.
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Step 6.1
Replace all occurrences of in with .
Step 6.2
Simplify the left side.
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Step 6.2.1
Simplify .
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Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Subtract from .
Step 7
Solve for in .
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Step 7.1
Move all terms not containing to the right side of the equation.
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Step 7.1.1
Add to both sides of the equation.
Step 7.1.2
Add and .
Step 7.2
Divide each term in by and simplify.
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Step 7.2.1
Divide each term in by .
Step 7.2.2
Simplify the left side.
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Step 7.2.2.1
Cancel the common factor of .
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Step 7.2.2.1.1
Cancel the common factor.
Step 7.2.2.1.2
Divide by .
Step 7.2.3
Simplify the right side.
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Step 7.2.3.1
Move the negative in front of the fraction.
Step 8
Solve the system of equations.
Step 9
List all of the solutions.