Facts About Systems of 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:

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 the lines are parallel and do not intersect at any points the solution is No Solutions.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

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

When the lines are intersecting at every point because they coincide and are the exact same line the solution is Infinite 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.