Algebra Examples

Solve by Addition/Elimination x+3y+2z=2 -2x-2y=-12 -x-2y-z=-4
Step 1
Choose two equations and eliminate one variable. In this case, eliminate .
Step 2
Eliminate from the system.
Tap for more steps...
Step 2.1
Multiply each equation by the value that makes the coefficients of opposite.
Step 2.2
Simplify.
Tap for more steps...
Step 2.2.1
Simplify the left side.
Tap for more steps...
Step 2.2.1.1
Simplify .
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 2.2.2
Simplify the right side.
Tap for more steps...
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
Eliminate from the system.
Tap for more steps...
Step 4.1
Multiply each equation by the value that makes the coefficients of opposite.
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
Apply the distributive property.
Step 4.2.1.1.2
Simplify.
Tap for more steps...
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.
Tap for more steps...
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
Eliminate from the system.
Tap for more steps...
Step 6.1
Multiply each equation by the value that makes the coefficients of opposite.
Step 6.2
Simplify.
Tap for more steps...
Step 6.2.1
Simplify the left side.
Tap for more steps...
Step 6.2.1.1
Simplify .
Tap for more steps...
Step 6.2.1.1.1
Apply the distributive property.
Step 6.2.1.1.2
Multiply.
Tap for more steps...
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.
Tap for more steps...
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