FACTS about Solving Systems of Linear Equations

Identify which method for solving systems is being described by this fact:

Equations must be written in slope-intercept form

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact:

The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact:

If one equation is isolated like y = 2x or

x = 7 - 4y then this method should be used.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact:

Use an isolated variable and plug that expression into the second equation in order to solve for the other variable. Plug that value back into the original isolated equation to solve for the second variable.

• 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 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:

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:

The solution to a system of equations must make both of the equations true.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

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

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