VOCABULARY

• Ordered Pair: identifies a point in the coordinate plane

• Linear Equation: a rule that defines a line in the coordinate plane– Slope-intercept Form:– Standard Form:

VOCABULARY

• System of Equations: a set of equations that are all satisfied by the same values of the variables– example: and are both true statements when and

• A solution of a system in two variables is an ordered pair that makes BOTH equations true– in the example above, the solution is

• Systems of Equations can have no solution, one solution or many solutions.

VOCABULARY

• Consistent Independent:– Has one solution– The lines intersect

• Consistent Dependent:– Has many solutions (infinitely many)– The lines are the same

• Inconsistent:– Has no solution– The lines are parallel

Objective: to find the solution to a system of equations using the substitution method

• Step 1: Solve one of the equations for a variable• Step 2: Substitute the solution into the OTHER

equation• Step 3: Solve the new equation from Step 2• Step 4: Plug the solution from Step 3 into the

equation from Step 1 and solve• Step 5: Check your answer – does the solution

make both equations true statements?

Substitution Method Example

• Using the same system from yesterday: and

• Step 1: Solving for we get • Step 2: Substituting this into we get • Step 3: Solving we get • Step 4: Plugging this into we get and

solving we get and find our solution is • Step 5: Check your answer – does the solution

make both equations true statements?

Guided Practice

and

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

and

Step 1:

Step 2:

Step 3:

Step 4:

Step 5: