Finite Math Examples

Evaluate Using the Given Value 0.42x+0.23y+0.15z=x , 0.27x+0.45y+0.37z=y , 0.31x+0.32y+0.48z , x+y+z=1
, , ,
Step 1
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from 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
Remove parentheses.
Step 2.2.1.2
Simplify each term.
Tap for more steps...
Step 2.2.1.2.1
Apply the distributive property.
Step 2.2.1.2.2
Simplify.
Tap for more steps...
Step 2.2.1.2.2.1
Multiply by .
Step 2.2.1.2.2.2
Multiply by .
Step 2.2.1.2.2.3
Multiply by .
Step 2.2.1.3
Simplify by adding terms.
Tap for more steps...
Step 2.2.1.3.1
Add and .
Step 2.2.1.3.2
Add and .
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
Simplify.
Tap for more steps...
Step 2.4.1.1.2.1
Multiply by .
Step 2.4.1.1.2.2
Multiply by .
Step 2.4.1.1.2.3
Multiply by .
Step 2.4.1.2
Simplify by adding terms.
Tap for more steps...
Step 2.4.1.2.1
Add and .
Step 2.4.1.2.2
Add and .
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 both sides of the equation.
Step 3.1.3
Subtract from .
Step 3.2
Divide each term in by and simplify.
Tap for more steps...
Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
Tap for more steps...
Step 3.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.2.3
Simplify the right side.
Tap for more steps...
Step 3.2.3.1
Simplify each term.
Tap for more steps...
Step 3.2.3.1.1
Factor out of .
Step 3.2.3.1.2
Factor out of .
Step 3.2.3.1.3
Separate fractions.
Step 3.2.3.1.4
Divide by .
Step 3.2.3.1.5
Divide by .
Step 3.2.3.1.6
Divide 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 .
Tap for more steps...
Step 4.2.1
Simplify the left side.
Tap for more steps...
Step 4.2.1.1
Simplify .
Tap for more steps...
Step 4.2.1.1.1
Simplify each term.
Tap for more steps...
Step 4.2.1.1.1.1
Apply the distributive property.
Step 4.2.1.1.1.2
Multiply by .
Step 4.2.1.1.1.3
Multiply by .
Step 4.2.1.1.2
Simplify by adding terms.
Tap for more steps...
Step 4.2.1.1.2.1
Add and .
Step 4.2.1.1.2.2
Subtract from .
Step 4.2.2
Simplify the right side.
Tap for more steps...
Step 4.2.2.1
Simplify .
Tap for more steps...
Step 4.2.2.1.1
Simplify each term.
Tap for more steps...
Step 4.2.2.1.1.1
Apply the distributive property.
Step 4.2.2.1.1.2
Multiply by .
Step 4.2.2.1.1.3
Multiply by .
Step 4.2.2.1.2
Simplify by adding terms.
Tap for more steps...
Step 4.2.2.1.2.1
Add and .
Step 4.2.2.1.2.2
Subtract from .
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
Apply the distributive property.
Step 4.4.1.1.2
Multiply by .
Step 4.4.1.1.3
Multiply by .
Step 4.4.1.2
Simplify by adding terms.
Tap for more steps...
Step 4.4.1.2.1
Add and .
Step 4.4.1.2.2
Subtract from .
Step 5
Solve for in .
Tap for more steps...
Step 5.1
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 5.1.1
Add to both sides of the equation.
Step 5.1.2
Add and .
Step 5.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Subtract from .
Step 5.3
Divide each term in by and simplify.
Tap for more steps...
Step 5.3.1
Divide each term in by .
Step 5.3.2
Simplify the left side.
Tap for more steps...
Step 5.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.3.2.1.1
Cancel the common factor.
Step 5.3.2.1.2
Divide by .
Step 5.3.3
Simplify the right side.
Tap for more steps...
Step 5.3.3.1
Divide by .
Step 6
Replace all occurrences of with in each equation.
Tap for more steps...
Step 6.1
Replace all occurrences of in with .
Step 6.2
Simplify the right side.
Tap for more steps...
Step 6.2.1
Simplify .
Tap for more steps...
Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Add and .
Step 6.3
Replace all occurrences of in with .
Step 6.4
Simplify the right side.
Tap for more steps...
Step 6.4.1
Simplify .
Tap for more steps...
Step 6.4.1.1
Multiply by .
Step 6.4.1.2
Subtract from .
Step 7
The solution to the system is the complete set of ordered pairs that are valid solutions.