Finite Math Examples

Solve by Substitution y=x^2 , y=3x+4
,
Step 1
Eliminate the equal sides of each equation and combine.
Step 2
Solve for .
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Subtract from both sides of the equation.
Step 2.3
Factor using the AC method.
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Step 2.3.1
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 2.3.2
Write the factored form using these integers.
Step 2.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.5
Set equal to and solve for .
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Step 2.5.1
Set equal to .
Step 2.5.2
Add to both sides of the equation.
Step 2.6
Set equal to and solve for .
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Step 2.6.1
Set equal to .
Step 2.6.2
Subtract from both sides of the equation.
Step 2.7
The final solution is all the values that make true.
Step 3
Evaluate when .
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Step 3.1
Substitute for .
Step 3.2
Simplify .
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Step 3.2.1
Multiply by .
Step 3.2.2
Add and .
Step 4
Evaluate when .
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Step 4.1
Substitute for .
Step 4.2
Simplify .
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Step 4.2.1
Multiply by .
Step 4.2.2
Add and .
Step 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 6
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 7