Trigonometry Examples

Solve by Substitution x-2y=0 , x^2+y^2=125
,
Step 1
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 product rule to .
Step 2.2.1.1.2
Raise to the power of .
Step 2.2.1.2
Add and .
Step 3
Solve for in .
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Step 3.1
Divide each term in by and simplify.
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Step 3.1.1
Divide each term in by .
Step 3.1.2
Simplify the left side.
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Step 3.1.2.1
Cancel the common factor of .
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Step 3.1.2.1.1
Cancel the common factor.
Step 3.1.2.1.2
Divide by .
Step 3.1.3
Simplify the right side.
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Step 3.1.3.1
Divide by .
Step 3.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.3
Simplify .
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Step 3.3.1
Rewrite as .
Step 3.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.4.1
First, use the positive value of the to find the first solution.
Step 3.4.2
Next, use the negative value of the to find the second solution.
Step 3.4.3
The complete solution is the result of both the positive and negative portions of the solution.
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
Multiply 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
Multiply 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