Systems Elimination Opposite Terms

To find the second variable, substitute the x or y you solved for into one of the ____.

• original equations

• one of the manipulated equations

• the top equation, always

• the bottom equation, always

Order the algorithm (steps) to elimination

• Align like terms vertically

• Determine the variable to eliminate

• multiply equation(s) to have opposite coefficients, if necessary

• add vertically

• Solve for variable

Identify which method for solving systems is being described by this fact: If like terms have a matching coefficient but not opposite values, take the opposite of every term in one equation.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: Equations must have like terms "stacked" up vertically, usually written in standard form.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: If like terms do not have a matching coefficient, multiplying one or both of the equations by a certain factor to transform the equations into a set of like terms with a matching set of coefficients.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: When solving the system a false statement results like 0 = 6 or 4 = -1 and the answer is No Solutions.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

When using any of the 3 methods to solve a system of linear equations the resulting solution is the same no matter which method is used.

• True; using any method will result in the correct solution.

• False; the solution varies because the solution depends on which method is used.

Identify which method for solving systems is being described by this fact: When solving the system a true statement results like 6 = 6 or 0 = 0 and the answer is Infinite Solutions.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

Solve by elimination 
2x+9y= -7 
6x-3y= 9 

• (-1, -1) 

• (2,-1)

• (1,1)

• (1,-1)

Solve by elimination:

3x+7y=23

-3x-7y=-17

• No solution

• (0, 3)

• (-3,3)

• (3,3)