Finite Math Examples

Solve Using a Matrix by Elimination 1/3x+1/2y=7 , 2/3x-5/2y=-14
,
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
Combine and .
Step 1.1.2
Combine and .
Step 1.2
Reorder terms.
Step 1.3
Simplify each term.
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Step 1.3.1
Combine and .
Step 1.3.2
Combine and .
Step 1.3.3
Move to the left of .
Step 1.4
Reorder terms.
Step 1.5
Remove parentheses.
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
Multiply each element of by to make the entry at a .
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Step 3.3.1
Multiply each element of by to make the entry at a .
Step 3.3.2
Simplify .
Step 3.4
Perform the row operation to make the entry at a .
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Step 3.4.1
Perform the row operation to make the entry at a .
Step 3.4.2
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.