Finite Math Examples

Solve by Substitution z=7x+11y , 0.5x+0.25y=117 , 0.5x+0.75y=207
, ,
Step 1
Solve for in .
Tap for more steps...
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
Tap for more steps...
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Tap for more steps...
Step 1.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
Tap for more steps...
Step 1.2.3.1
Simplify each term.
Tap for more steps...
Step 1.2.3.1.1
Divide by .
Step 1.2.3.1.2
Move the negative in front of the fraction.
Step 1.2.3.1.3
Factor out of .
Step 1.2.3.1.4
Factor out of .
Step 1.2.3.1.5
Separate fractions.
Step 1.2.3.1.6
Divide by .
Step 1.2.3.1.7
Cancel the common factor of .
Tap for more steps...
Step 1.2.3.1.7.1
Factor out of .
Step 1.2.3.1.7.2
Cancel the common factor.
Step 1.2.3.1.7.3
Rewrite the expression.
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 right 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
Apply the distributive property.
Step 2.2.1.1.2
Multiply by .
Step 2.2.1.1.3
Multiply .
Tap for more steps...
Step 2.2.1.1.3.1
Multiply by .
Step 2.2.1.1.3.2
Combine and .
Step 2.2.1.1.4
Move the negative in front of the fraction.
Step 2.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.3
Simplify terms.
Tap for more steps...
Step 2.2.1.3.1
Combine and .
Step 2.2.1.3.2
Combine the numerators over the common denominator.
Step 2.2.1.4
Simplify each term.
Tap for more steps...
Step 2.2.1.4.1
Simplify the numerator.
Tap for more steps...
Step 2.2.1.4.1.1
Factor out of .
Tap for more steps...
Step 2.2.1.4.1.1.1
Factor out of .
Step 2.2.1.4.1.1.2
Factor out of .
Step 2.2.1.4.1.1.3
Factor out of .
Step 2.2.1.4.1.2
Multiply by .
Step 2.2.1.4.1.3
Add and .
Step 2.2.1.4.2
Move to the left of .
Step 2.3
Replace all occurrences of in with .
Step 2.4
Simplify the left side.
Tap for more steps...
Step 2.4.1
Simplify .
Tap for more steps...
Step 2.4.1.1
Simplify each term.
Tap for more steps...
Step 2.4.1.1.1
Apply the distributive property.
Step 2.4.1.1.2
Multiply by .
Step 2.4.1.1.3
Cancel the common factor of .
Tap for more steps...
Step 2.4.1.1.3.1
Move the leading negative in into the numerator.
Step 2.4.1.1.3.2
Factor out of .
Step 2.4.1.1.3.3
Cancel the common factor.
Step 2.4.1.1.3.4
Rewrite the expression.
Step 2.4.1.1.4
Move the negative in front of the fraction.
Step 2.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.4.1.3
Simplify terms.
Tap for more steps...
Step 2.4.1.3.1
Combine and .
Step 2.4.1.3.2
Combine the numerators over the common denominator.
Step 2.4.1.4
Simplify each term.
Tap for more steps...
Step 2.4.1.4.1
Simplify the numerator.
Tap for more steps...
Step 2.4.1.4.1.1
Factor out of .
Tap for more steps...
Step 2.4.1.4.1.1.1
Move .
Step 2.4.1.4.1.1.2
Factor out of .
Step 2.4.1.4.1.1.3
Factor out of .
Step 2.4.1.4.1.1.4
Factor out of .
Step 2.4.1.4.1.2
Combine exponents.
Tap for more steps...
Step 2.4.1.4.1.2.1
Multiply by .
Step 2.4.1.4.1.2.2
Multiply by .
Step 2.4.1.4.2
Cancel the common factor of and .
Tap for more steps...
Step 2.4.1.4.2.1
Factor out of .
Step 2.4.1.4.2.2
Cancel the common factors.
Tap for more steps...
Step 2.4.1.4.2.2.1
Factor out of .
Step 2.4.1.4.2.2.2
Cancel the common factor.
Step 2.4.1.4.2.2.3
Rewrite the expression.
Step 3
Solve for in .
Tap for more steps...
Step 3.1
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Subtract from .
Step 3.2
Multiply both sides of the equation by .
Step 3.3
Simplify both sides of the equation.
Tap for more steps...
Step 3.3.1
Simplify the left side.
Tap for more steps...
Step 3.3.1.1
Cancel the common factor of .
Tap for more steps...
Step 3.3.1.1.1
Cancel the common factor.
Step 3.3.1.1.2
Rewrite the expression.
Step 3.3.2
Simplify the right side.
Tap for more steps...
Step 3.3.2.1
Multiply by .
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 the right side.
Tap for more steps...
Step 4.2.1
Simplify .
Tap for more steps...
Step 4.2.1.1
Multiply by .
Step 4.2.1.2
Divide by .
Step 4.2.1.3
Add and .
Step 4.3
Replace all occurrences of in with .
Step 4.4
Simplify the right side.
Tap for more steps...
Step 4.4.1
Simplify .
Tap for more steps...
Step 4.4.1.1
Simplify each term.
Tap for more steps...
Step 4.4.1.1.1
Divide by .
Step 4.4.1.1.2
Multiply by .
Step 4.4.1.2
Subtract from .
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: