Finite Math Examples

Solve by Substitution 2x+y-7z=-15 , 4x+3y+5z=5 , x+y+6z=10
, ,
Step 1
Move all terms not containing to the right side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Add to 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
Simplify.
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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.
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Step 2.2.1.2.1
Subtract from .
Step 2.2.1.2.2
Add and .
Step 2.3
Replace all occurrences of in with .
Step 2.4
Simplify the left side.
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Step 2.4.1
Simplify .
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Step 2.4.1.1
Remove parentheses.
Step 2.4.1.2
Subtract from .
Step 2.4.1.3
Add and .
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
Add to both sides of the equation.
Step 3.1.2
Subtract from both sides of the equation.
Step 3.1.3
Add and .
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
Dividing two negative values results in a positive value.
Step 3.2.2.2
Divide by .
Step 3.2.3
Simplify the right side.
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Step 3.2.3.1
Simplify each term.
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Step 3.2.3.1.1
Divide by .
Step 3.2.3.1.2
Move the negative one from the denominator of .
Step 3.2.3.1.3
Rewrite as .
Step 3.2.3.1.4
Multiply 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
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 4.2.1.1.3
Multiply by .
Step 4.2.1.2
Simplify by adding terms.
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Step 4.2.1.2.1
Combine the opposite terms in .
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Step 4.2.1.2.1.1
Add and .
Step 4.2.1.2.1.2
Add and .
Step 4.2.1.2.2
Subtract from .
Step 4.3
Replace all occurrences of in with .
Step 4.4
Simplify the right side.
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Step 4.4.1
Simplify .
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Step 4.4.1.1
Simplify each term.
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Step 4.4.1.1.1
Apply the distributive property.
Step 4.4.1.1.2
Multiply by .
Step 4.4.1.1.3
Multiply by .
Step 4.4.1.2
Simplify by adding terms.
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Step 4.4.1.2.1
Add and .
Step 4.4.1.2.2
Add and .
Step 5
Remove any equations from the system that are always true.