Algebra Examples

Solve the System of Equations y=x^2+3 , y=-2x^2+3
,
Step 1
Eliminate the equal sides of each equation and combine.
Step 2
Solve for .
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Step 2.1
Move all terms containing to the left side of the equation.
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Step 2.1.1
Add to both sides of the equation.
Step 2.1.2
Add and .
Step 2.2
Move all terms not containing to the right side of the equation.
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Step 2.2.1
Subtract from both sides of the equation.
Step 2.2.2
Subtract from .
Step 2.3
Divide each term in by and simplify.
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Step 2.3.1
Divide each term in by .
Step 2.3.2
Simplify the left side.
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Step 2.3.2.1
Cancel the common factor of .
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Step 2.3.2.1.1
Cancel the common factor.
Step 2.3.2.1.2
Divide by .
Step 2.3.3
Simplify the right side.
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Step 2.3.3.1
Divide by .
Step 2.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.5
Simplify .
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Step 2.5.1
Rewrite as .
Step 2.5.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.5.3
Plus or minus is .
Step 3
Evaluate when .
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Step 3.1
Substitute for .
Step 3.2
Substitute for in and solve for .
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Step 3.2.1
Remove parentheses.
Step 3.2.2
Simplify .
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Step 3.2.2.1
Simplify each term.
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Step 3.2.2.1.1
Raising to any positive power yields .
Step 3.2.2.1.2
Multiply by .
Step 3.2.2.2
Add and .
Step 4
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 5
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 6