Finite Math Examples

Find the Inverse x-5y=-4
Step 1
Subtract from both sides of the equation.
Step 2
Divide each term in by and simplify.
Tap for more steps...
Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
Tap for more steps...
Step 2.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
Tap for more steps...
Step 2.3.1
Simplify each term.
Tap for more steps...
Step 2.3.1.1
Dividing two negative values results in a positive value.
Step 2.3.1.2
Dividing two negative values results in a positive value.
Step 3
Interchange the variables.
Step 4
Solve for .
Tap for more steps...
Step 4.1
Rewrite the equation as .
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Multiply both sides of the equation by .
Step 4.4
Simplify both sides of the equation.
Tap for more steps...
Step 4.4.1
Simplify the left side.
Tap for more steps...
Step 4.4.1.1
Cancel the common factor of .
Tap for more steps...
Step 4.4.1.1.1
Cancel the common factor.
Step 4.4.1.1.2
Rewrite the expression.
Step 4.4.2
Simplify the right side.
Tap for more steps...
Step 4.4.2.1
Simplify .
Tap for more steps...
Step 4.4.2.1.1
Apply the distributive property.
Step 4.4.2.1.2
Cancel the common factor of .
Tap for more steps...
Step 4.4.2.1.2.1
Move the leading negative in into the numerator.
Step 4.4.2.1.2.2
Cancel the common factor.
Step 4.4.2.1.2.3
Rewrite the expression.
Step 5
Replace with to show the final answer.
Step 6
Verify if is the inverse of .
Tap for more steps...
Step 6.1
To verify the inverse, check if and .
Step 6.2
Evaluate .
Tap for more steps...
Step 6.2.1
Set up the composite result function.
Step 6.2.2
Evaluate by substituting in the value of into .
Step 6.2.3
Simplify each term.
Tap for more steps...
Step 6.2.3.1
Apply the distributive property.
Step 6.2.3.2
Cancel the common factor of .
Tap for more steps...
Step 6.2.3.2.1
Cancel the common factor.
Step 6.2.3.2.2
Rewrite the expression.
Step 6.2.3.3
Cancel the common factor of .
Tap for more steps...
Step 6.2.3.3.1
Cancel the common factor.
Step 6.2.3.3.2
Rewrite the expression.
Step 6.2.4
Combine the opposite terms in .
Tap for more steps...
Step 6.2.4.1
Subtract from .
Step 6.2.4.2
Add and .
Step 6.3
Evaluate .
Tap for more steps...
Step 6.3.1
Set up the composite result function.
Step 6.3.2
Evaluate by substituting in the value of into .
Step 6.3.3
Combine the numerators over the common denominator.
Step 6.3.4
Combine the opposite terms in .
Tap for more steps...
Step 6.3.4.1
Subtract from .
Step 6.3.4.2
Add and .
Step 6.3.5
Cancel the common factor of .
Tap for more steps...
Step 6.3.5.1
Cancel the common factor.
Step 6.3.5.2
Divide by .
Step 6.4
Since and , then is the inverse of .