Finite Math Examples

Solve in Terms of the Arbitrary Variable k 5x+5y+3z=-4 , 8x+2y+5z=-5 , 11x-y+hz=k
, ,
Step 1
Solve the equation for .
Tap for more steps...
Move all terms not containing to the right side of the equation.
Tap for more steps...
Subtract from both sides of the equation.
Subtract from both sides of the equation.
Divide each term in by and simplify.
Tap for more steps...
Divide each term in by .
Simplify the left side.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Divide by .
Simplify the right side.
Tap for more steps...
Simplify each term.
Tap for more steps...
Move the negative in front of the fraction.
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Move the negative in front of the fraction.
Step 2
Solve the equation for .
Tap for more steps...
Simplify .
Tap for more steps...
Simplify each term.
Tap for more steps...
Apply the distributive property.
Simplify.
Tap for more steps...
Multiply .
Tap for more steps...
Multiply by .
Combine and .
Multiply by .
Multiply by .
Multiply .
Tap for more steps...
Multiply by .
Combine and .
Multiply by .
Simplify each term.
Tap for more steps...
Move the negative in front of the fraction.
Move the negative in front of the fraction.
Add and .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Combine the numerators over the common denominator.
Multiply by .
Add and .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Multiply by .
Factor out of .
Rewrite as .
Factor out of .
Factor out of .
Factor out of .
Simplify the expression.
Tap for more steps...
Rewrite as .
Move the negative in front of the fraction.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Tap for more steps...
Simplify the left side.
Tap for more steps...
Simplify .
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply.
Tap for more steps...
Multiply by .
Multiply by .
Simplify the right side.
Tap for more steps...
Multiply by .
Move all terms not containing to the right side of the equation.
Tap for more steps...
Subtract from both sides of the equation.
Add to both sides of the equation.
Subtract from .
Divide each term in by and simplify.
Tap for more steps...
Divide each term in by .
Simplify the left side.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Divide by .
Simplify the right side.
Tap for more steps...
Move the negative in front of the fraction.
Step 3
Solve the equation for .
Tap for more steps...
Simplify .
Tap for more steps...
Simplify each term.
Tap for more steps...
Find the common denominator.
Tap for more steps...
Write as a fraction with denominator .
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Multiply .
Tap for more steps...
Multiply by .
Multiply by .
Apply the distributive property.
Cancel the common factor of .
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Tap for more steps...
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Multiply by .
Add and .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Combine the numerators over the common denominator.
Multiply by .
Subtract from .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Tap for more steps...
Multiply by .
Multiply by .
Multiply .
Tap for more steps...
Multiply by .
Combine and .
Move the negative in front of the fraction.
Apply the distributive property.
Multiply .
Tap for more steps...
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Multiply by .
Multiply by .
Simplify terms.
Tap for more steps...
Add and .
Subtract from .
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Move all terms not containing to the right side of the equation.
Tap for more steps...
Add to both sides of the equation.
Add to both sides of the equation.
Divide each term in by and simplify.
Tap for more steps...
Divide each term in by .
Simplify the left side.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Divide by .
Simplify the right side.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Divide by .
Step 4
Solve the equation for .
Tap for more steps...
Simplify .
Tap for more steps...
Simplify each term.
Tap for more steps...
Find the common denominator.
Tap for more steps...
Write as a fraction with denominator .
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Multiply .
Tap for more steps...
Multiply by .
Multiply by .
Apply the distributive property.
Cancel the common factor of .
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Tap for more steps...
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Multiply by .
Add and .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Combine the numerators over the common denominator.
Multiply by .
Subtract from .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Cancel the common factor of .
Tap for more steps...
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Cancel the common factor of .
Tap for more steps...
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Multiply by .
Multiply by .
Simplify terms.
Tap for more steps...
Subtract from .
Add and .
Cancel the common factor of and .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Subtract from .
Subtract from .
Since , the equation will always be true.
Always true
Always true
Step 5
Simplify the right side.
Tap for more steps...
Reorder and .
Always true
Always true