Precalculus Examples

Solve by Substitution x^2+y^2=116 , x-y=-6
,
Step 1
Add to both sides of the equation.
Step 2
Replace all occurrences of with in each equation.
Tap for more steps...
Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
Tap for more steps...
Step 2.2.1
Simplify .
Tap for more steps...
Step 2.2.1.1
Simplify each term.
Tap for more steps...
Step 2.2.1.1.1
Rewrite as .
Step 2.2.1.1.2
Expand using the FOIL Method.
Tap for more steps...
Step 2.2.1.1.2.1
Apply the distributive property.
Step 2.2.1.1.2.2
Apply the distributive property.
Step 2.2.1.1.2.3
Apply the distributive property.
Step 2.2.1.1.3
Simplify and combine like terms.
Tap for more steps...
Step 2.2.1.1.3.1
Simplify each term.
Tap for more steps...
Step 2.2.1.1.3.1.1
Multiply by .
Step 2.2.1.1.3.1.2
Move to the left of .
Step 2.2.1.1.3.1.3
Multiply by .
Step 2.2.1.1.3.2
Subtract from .
Step 2.2.1.2
Add and .
Step 3
Solve for in .
Tap for more steps...
Step 3.1
Subtract from both sides of the equation.
Step 3.2
Subtract from .
Step 3.3
Factor the left side of the equation.
Tap for more steps...
Step 3.3.1
Factor out of .
Tap for more steps...
Step 3.3.1.1
Factor out of .
Step 3.3.1.2
Factor out of .
Step 3.3.1.3
Factor out of .
Step 3.3.1.4
Factor out of .
Step 3.3.1.5
Factor out of .
Step 3.3.2
Let . Substitute for all occurrences of .
Step 3.3.3
Factor using the AC method.
Tap for more steps...
Step 3.3.3.1
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 3.3.3.2
Write the factored form using these integers.
Step 3.3.4
Factor.
Tap for more steps...
Step 3.3.4.1
Replace all occurrences of with .
Step 3.3.4.2
Remove unnecessary parentheses.
Step 3.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.5
Set equal to and solve for .
Tap for more steps...
Step 3.5.1
Set equal to .
Step 3.5.2
Add to both sides of the equation.
Step 3.6
Set equal to and solve for .
Tap for more steps...
Step 3.6.1
Set equal to .
Step 3.6.2
Subtract from both sides of the equation.
Step 3.7
The final solution is all the values that make true.
Step 4
Replace all occurrences of with in each equation.
Tap for more steps...
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify .
Tap for more steps...
Step 4.2.1
Simplify the left side.
Tap for more steps...
Step 4.2.1.1
Remove parentheses.
Step 4.2.2
Simplify the right side.
Tap for more steps...
Step 4.2.2.1
Add and .
Step 5
Replace all occurrences of with in each equation.
Tap for more steps...
Step 5.1
Replace all occurrences of in with .
Step 5.2
Simplify .
Tap for more steps...
Step 5.2.1
Simplify the left side.
Tap for more steps...
Step 5.2.1.1
Remove parentheses.
Step 5.2.2
Simplify the right side.
Tap for more steps...
Step 5.2.2.1
Subtract from .
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