Finite Math Examples

Solve by Substitution xy=48 , 2x-y=-4
,
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 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 .
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Step 2.2.1.1
Combine and .
Step 2.2.1.2
Multiply by .
Step 3
Solve for in .
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Step 3.1
Find the LCD of the terms in the equation.
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Step 3.1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.1.2
The LCM of one and any expression is the expression.
y
y
Step 3.2
Multiply each term in by to eliminate the fractions.
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Step 3.2.1
Multiply each term in by .
Step 3.2.2
Simplify the left side.
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Step 3.2.2.1
Simplify each term.
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Step 3.2.2.1.1
Cancel the common factor of .
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Step 3.2.2.1.1.1
Cancel the common factor.
Step 3.2.2.1.1.2
Rewrite the expression.
Step 3.2.2.1.2
Multiply by by adding the exponents.
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Step 3.2.2.1.2.1
Move .
Step 3.2.2.1.2.2
Multiply by .
Step 3.3
Solve the equation.
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Step 3.3.1
Add to both sides of the equation.
Step 3.3.2
Factor the left side of the equation.
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Step 3.3.2.1
Factor out of .
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Step 3.3.2.1.1
Move .
Step 3.3.2.1.2
Factor out of .
Step 3.3.2.1.3
Factor out of .
Step 3.3.2.1.4
Rewrite as .
Step 3.3.2.1.5
Factor out of .
Step 3.3.2.1.6
Factor out of .
Step 3.3.2.2
Factor.
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Step 3.3.2.2.1
Factor using the AC method.
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Step 3.3.2.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.3.2.2.1.2
Write the factored form using these integers.
Step 3.3.2.2.2
Remove unnecessary parentheses.
Step 3.3.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.3.4
Set equal to and solve for .
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Step 3.3.4.1
Set equal to .
Step 3.3.4.2
Add to both sides of the equation.
Step 3.3.5
Set equal to and solve for .
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Step 3.3.5.1
Set equal to .
Step 3.3.5.2
Subtract from both sides of the equation.
Step 3.3.6
The final solution is all the values that make true.
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 right side.
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Step 4.2.1
Divide by .
Step 5
Replace all occurrences of with in each equation.
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Step 5.1
Replace all occurrences of in with .
Step 5.2
Simplify the right side.
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Step 5.2.1
Divide by .
Step 6
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 7
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 8