Finite Math Examples

Solve by Substitution x+2y+z=-2 , 5x+3y-z=-11 , x+5y+3z=-5
, ,
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
Simplify each term.
Tap for more steps...
Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Simplify.
Tap for more steps...
Step 2.2.1.1.2.1
Multiply by .
Step 2.2.1.1.2.2
Multiply by .
Step 2.2.1.1.2.3
Multiply by .
Step 2.2.1.2
Simplify by adding terms.
Tap for more steps...
Step 2.2.1.2.1
Add and .
Step 2.2.1.2.2
Subtract from .
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
Add and .
Step 2.4.1.2
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
Add to both sides of the equation.
Step 3.1.2
Subtract from both sides of the equation.
Step 3.1.3
Add and .
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
Divide by .
Step 3.2.3.1.2
Move the negative in front of the fraction.
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 left side.
Tap for more steps...
Step 4.2.1
Simplify .
Tap for more steps...
Step 4.2.1.1
Simplify each term.
Tap for more steps...
Step 4.2.1.1.1
Apply the distributive property.
Step 4.2.1.1.2
Multiply by .
Step 4.2.1.1.3
Multiply .
Tap for more steps...
Step 4.2.1.1.3.1
Multiply by .
Step 4.2.1.1.3.2
Combine and .
Step 4.2.1.1.3.3
Multiply by .
Step 4.2.1.2
Add and .
Step 4.2.1.3
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.4
Simplify terms.
Tap for more steps...
Step 4.2.1.4.1
Combine and .
Step 4.2.1.4.2
Combine the numerators over the common denominator.
Step 4.2.1.5
Simplify each term.
Tap for more steps...
Step 4.2.1.5.1
Simplify the numerator.
Tap for more steps...
Step 4.2.1.5.1.1
Factor out of .
Tap for more steps...
Step 4.2.1.5.1.1.1
Factor out of .
Step 4.2.1.5.1.1.2
Factor out of .
Step 4.2.1.5.1.1.3
Factor out of .
Step 4.2.1.5.1.2
Multiply by .
Step 4.2.1.5.1.3
Subtract from .
Step 4.2.1.5.1.4
Multiply by .
Step 4.2.1.5.2
Move the negative in front of the fraction.
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 .
Tap for more steps...
Step 4.4.1.1.3.1
Multiply by .
Step 4.4.1.1.3.2
Combine and .
Step 4.4.1.1.3.3
Multiply by .
Step 4.4.1.2
Simplify by adding numbers.
Tap for more steps...
Step 4.4.1.2.1
Add and .
Step 4.4.1.2.2
Add and .
Step 4.4.1.3
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.4
Simplify terms.
Tap for more steps...
Step 4.4.1.4.1
Combine and .
Step 4.4.1.4.2
Combine the numerators over the common denominator.
Step 4.4.1.5
Simplify the numerator.
Tap for more steps...
Step 4.4.1.5.1
Factor out of .
Tap for more steps...
Step 4.4.1.5.1.1
Factor out of .
Step 4.4.1.5.1.2
Factor out of .
Step 4.4.1.5.1.3
Factor out of .
Step 4.4.1.5.2
Multiply by .
Step 4.4.1.5.3
Subtract from .
Step 4.4.1.6
Multiply by .
Step 5
Solve for in .
Tap for more steps...
Step 5.1
Move all terms not containing to the right 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
Multiply both sides of the equation by .
Step 5.3
Simplify both sides of the equation.
Tap for more steps...
Step 5.3.1
Simplify the left side.
Tap for more steps...
Step 5.3.1.1
Simplify .
Tap for more steps...
Step 5.3.1.1.1
Cancel the common factor of .
Tap for more steps...
Step 5.3.1.1.1.1
Move the leading negative in into the numerator.
Step 5.3.1.1.1.2
Move the leading negative in into the numerator.
Step 5.3.1.1.1.3
Factor out of .
Step 5.3.1.1.1.4
Cancel the common factor.
Step 5.3.1.1.1.5
Rewrite the expression.
Step 5.3.1.1.2
Cancel the common factor of .
Tap for more steps...
Step 5.3.1.1.2.1
Factor out of .
Step 5.3.1.1.2.2
Cancel the common factor.
Step 5.3.1.1.2.3
Rewrite the expression.
Step 5.3.1.1.3
Multiply.
Tap for more steps...
Step 5.3.1.1.3.1
Multiply by .
Step 5.3.1.1.3.2
Multiply by .
Step 5.3.2
Simplify the right side.
Tap for more steps...
Step 5.3.2.1
Simplify .
Tap for more steps...
Step 5.3.2.1.1
Cancel the common factor of .
Tap for more steps...
Step 5.3.2.1.1.1
Move the leading negative in into the numerator.
Step 5.3.2.1.1.2
Factor out of .
Step 5.3.2.1.1.3
Cancel the common factor.
Step 5.3.2.1.1.4
Rewrite the expression.
Step 5.3.2.1.2
Multiply 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
Divide by .
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
Simplify each term.
Tap for more steps...
Step 6.4.1.1.1
Cancel the common factor of and .
Tap for more steps...
Step 6.4.1.1.1.1
Factor out of .
Step 6.4.1.1.1.2
Cancel the common factors.
Tap for more steps...
Step 6.4.1.1.1.2.1
Factor out of .
Step 6.4.1.1.1.2.2
Cancel the common factor.
Step 6.4.1.1.1.2.3
Rewrite the expression.
Step 6.4.1.1.1.2.4
Divide by .
Step 6.4.1.1.2
Multiply .
Tap for more steps...
Step 6.4.1.1.2.1
Multiply by .
Step 6.4.1.1.2.2
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.
Step 8
The result can be shown in multiple forms.
Point Form:
Equation Form: