Finite Math Examples

Solve Using an Augmented Matrix 27x*1+8x*2+43x*3=29 , 15x*1-19x*2+31x*3=16 , 22x*1+18x*2-12x*3=-17
, ,
Step 1
Move variables to the left and constant terms to the right.
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Step 1.1
Simplify each term.
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Step 1.1.1
Multiply by .
Step 1.1.2
Multiply by .
Step 1.1.3
Multiply by .
Step 1.2
Add and .
Step 1.3
Add and .
Step 1.4
Simplify each term.
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Step 1.4.1
Multiply by .
Step 1.4.2
Multiply by .
Step 1.4.3
Multiply by .
Step 1.5
Subtract from .
Step 1.6
Add and .
Step 1.7
Simplify each term.
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Step 1.7.1
Multiply by .
Step 1.7.2
Multiply by .
Step 1.7.3
Multiply by .
Step 1.8
Combine the opposite terms in .
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Step 1.8.1
Subtract from .
Step 1.8.2
Add and .
Step 2
Write the system as a matrix.
Step 3
Find the reduced row echelon form.
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Step 3.1
Multiply each element of by to make the entry at a .
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Step 3.1.1
Multiply each element of by to make the entry at a .
Step 3.1.2
Simplify .
Step 3.2
Perform the row operation to make the entry at a .
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Step 3.2.1
Perform the row operation to make the entry at a .
Step 3.2.2
Simplify .
Step 3.3
Perform the row operation to make the entry at a .
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Step 3.3.1
Perform the row operation to make the entry at a .
Step 3.3.2
Simplify .
Step 3.4
Multiply each element of by to make the entry at a .
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Step 3.4.1
Multiply each element of by to make the entry at a .
Step 3.4.2
Simplify .
Step 3.5
Perform the row operation to make the entry at a .
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Step 3.5.1
Perform the row operation to make the entry at a .
Step 3.5.2
Simplify .
Step 3.6
Perform the row operation to make the entry at a .
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Step 3.6.1
Perform the row operation to make the entry at a .
Step 3.6.2
Simplify .
Step 4
Use the result matrix to declare the final solution to the system of equations.
Step 5
The solution is the set of ordered pairs that make the system true.