Finite Math Examples

Solve in Terms of the Arbitrary Variable u 8x+5y+u=7 , x+6y+v=9 , -32x-2y+m=0
, ,
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.
Move the negative in front of the fraction.
Step 2
Solve the equation for .
Tap for more steps...
Simplify .
Tap for more steps...
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 .
Simplify terms.
Tap for more steps...
Combine and .
Combine the numerators over the common denominator.
Move to the left of .
Multiply both sides by .
Simplify.
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...
Cancel the common factor.
Rewrite the expression.
Simplify the expression.
Tap for more steps...
Move .
Reorder and .
Simplify the right side.
Tap for more steps...
Multiply by .
Solve for .
Tap for more steps...
Move all terms not containing to the right side of the equation.
Tap for more steps...
Add to both sides of the equation.
Subtract from both sides of the equation.
Subtract from 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...
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Simplify.
Tap for more steps...
Combine and .
Multiply .
Tap for more steps...
Multiply by .
Combine and .
Multiply by .
Multiply .
Tap for more steps...
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.
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 .
Subtract from .
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 .
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Move the negative in front of the fraction.
Cancel the common factor of .
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Combine and .
Multiply by .
Apply the distributive property.
Simplify.
Tap for more steps...
Combine and .
Multiply .
Tap for more steps...
Multiply by .
Combine and .
Multiply by .
Multiply .
Tap for more steps...
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.
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Simplify.
Tap for more steps...
Multiply by .
Multiply by .
Multiply by .
Simplify terms.
Tap for more steps...
Subtract from .
Add and .
Subtract from .
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Tap for more steps...
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps...
Move to the left of .
Apply the distributive property.
Simplify.
Tap for more steps...
Multiply by .
Multiply by .
Multiply by .
Set the numerator equal to zero.
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.
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...
Move the negative in front of the fraction.
Step 4
Solve the equation for .
Tap for more steps...
Simplify .
Tap for more steps...
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Simplify.
Tap for more steps...
Combine and .
Multiply .
Tap for more steps...
Multiply by .
Combine and .
Multiply by .
Multiply .
Tap for more steps...
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.
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 .
Subtract from .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Tap for more steps...
Combine and .
Combine the numerators over the common denominator.
Combine the numerators over the common denominator.
Multiply by .
Subtract from .
Factor out of .
Tap for more steps...
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Tap for more steps...
Rewrite as .
Move the negative in front of the fraction.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Simplify.
Tap for more steps...
Combine and .
Multiply .
Tap for more steps...
Multiply by .
Combine and .
Multiply by .
Multiply .
Tap for more steps...
Combine and .
Multiply by .
Move the negative in front of the fraction.
Multiply the numerator by the reciprocal of the denominator.
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.
Combine the numerators over the common denominator.
Simplify each term.
Tap for more steps...
Apply the distributive property.
Simplify.
Tap for more steps...
Multiply by .
Multiply by .
Multiply by .
Simplify terms.
Tap for more steps...
Combine the opposite terms in .
Tap for more steps...
Subtract from .
Add and .
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 .
Subtract from .
Add and .
Since , the equation will always be true.
Always true
Always true
Step 5
Simplify the right side.
Tap for more steps...
Simplify .
Tap for more steps...
Combine the numerators over the common denominator.
Always true
Simplify each term.
Tap for more steps...
Apply the distributive property.
Always true
Simplify.
Tap for more steps...
Combine and .
Always true
Multiply .
Tap for more steps...
Multiply by .
Always true
Combine and .
Always true
Multiply by .
Always true
Always true
Multiply .
Tap for more steps...
Combine and .
Always true
Multiply by .
Always true
Always true
Always true
Simplify each term.
Tap for more steps...
Move the negative in front of the fraction.
Always true
Move the negative in front of the fraction.
Always true
Always true
Always true
To write as a fraction with a common denominator, multiply by .
Always true
Combine and .
Always true
Combine the numerators over the common denominator.
Always true
Simplify the numerator.
Tap for more steps...
Multiply by .
Always true
Subtract from .
Always true
Always true
Move the negative in front of the fraction.
Always true
To write as a fraction with a common denominator, multiply by .
Always true
Combine and .
Always true
Combine the numerators over the common denominator.
Always true
Combine the numerators over the common denominator.
Always true
Multiply by .
Always true
Subtract from .
Always true
Factor out of .
Tap for more steps...
Factor out of .
Always true
Factor out of .
Always true
Factor out of .
Always true
Factor out of .
Always true
Factor out of .
Always true
Always true
Factor out of .
Always true
Factor out of .
Always true
Factor out of .
Always true
Rewrite as .
Always true
Factor out of .
Always true
Simplify the expression.
Tap for more steps...
Rewrite as .
Always true
Move the negative in front of the fraction.
Always true
Always true
Multiply the numerator by the reciprocal of the denominator.
Always true
Cancel the common factor of .
Tap for more steps...
Move the leading negative in into the numerator.
Always true
Factor out of .
Always true
Cancel the common factor.
Always true
Rewrite the expression.
Always true
Always true
Move the negative in front of the fraction.
Always true
Always true
Always true