Finite Math Examples

Solve by Substitution x+2z=4 , 11/2x+y+10z=19 , 4y-4z=-12
, ,
Step 1
Subtract from both sides of the equation.
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
Simplify each term.
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Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Cancel the common factor of .
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Step 2.2.1.1.2.1
Factor out of .
Step 2.2.1.1.2.2
Cancel the common factor.
Step 2.2.1.1.2.3
Rewrite the expression.
Step 2.2.1.1.3
Multiply by .
Step 2.2.1.1.4
Cancel the common factor of .
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Step 2.2.1.1.4.1
Factor out of .
Step 2.2.1.1.4.2
Cancel the common factor.
Step 2.2.1.1.4.3
Rewrite the expression.
Step 2.2.1.1.5
Multiply by .
Step 2.2.1.2
Add and .
Step 3
Move all terms not containing to the right side of the equation.
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Step 3.1
Subtract from both sides of the equation.
Step 3.2
Add to both sides of the equation.
Step 3.3
Subtract from .
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
Simplify each term.
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Step 4.2.1.1.1
Apply the distributive property.
Step 4.2.1.1.2
Multiply by .
Step 4.2.1.2
Combine the opposite terms in .
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Step 4.2.1.2.1
Subtract from .
Step 4.2.1.2.2
Add and .
Step 5
Remove any equations from the system that are always true.