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Algebra Examples
Step 1
Choose two equations and eliminate one variable. In this case, eliminate .
Step 2
Step 2.1
Multiply each equation by the value that makes the coefficients of opposite.
Step 2.2
Simplify.
Step 2.2.1
Simplify the left side.
Step 2.2.1.1
Simplify .
Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Simplify.
Step 2.2.1.1.2.1
Multiply by .
Step 2.2.1.1.2.2
Multiply by .
Step 2.2.2
Simplify the right side.
Step 2.2.2.1
Multiply by .
Step 2.3
Add the two equations together to eliminate from the system.
Step 2.4
The resultant equation has eliminated.
Step 3
Choose another two equations and eliminate .
Step 4
Step 4.1
Multiply each equation by the value that makes the coefficients of opposite.
Step 4.2
Simplify.
Step 4.2.1
Simplify the left side.
Step 4.2.1.1
Simplify .
Step 4.2.1.1.1
Apply the distributive property.
Step 4.2.1.1.2
Simplify.
Step 4.2.1.1.2.1
Multiply by .
Step 4.2.1.1.2.2
Multiply by .
Step 4.2.1.1.2.3
Multiply by .
Step 4.2.2
Simplify the right side.
Step 4.2.2.1
Multiply by .
Step 4.3
Add the two equations together to eliminate from the system.
Step 4.4
The resultant equation has eliminated.
Step 5
Take the resultant equations and eliminate another variable. In this case, eliminate .
Step 6
Step 6.1
Multiply each equation by the value that makes the coefficients of opposite.
Step 6.2
Simplify.
Step 6.2.1
Simplify the left side.
Step 6.2.1.1
Simplify .
Step 6.2.1.1.1
Apply the distributive property.
Step 6.2.1.1.2
Multiply.
Step 6.2.1.1.2.1
Multiply by .
Step 6.2.1.1.2.2
Multiply by .
Step 6.2.2
Simplify the right side.
Step 6.2.2.1
Multiply by .
Step 6.3
Add the two equations together to eliminate from the system.
Step 6.4
The resultant equation has eliminated.
Step 7
Because the resultant equation includes no variables and is true, the system of equations has an infinite number of solutions.
Infinite number of solutions