When 2 lines are drawn on the same graph, there are 3 possible outcomes.

• The lines intersect

• The lines don't intersect

• The lines are on top of each other

For lines not to intersect at all...

• The lines must be parallel

• If the lines are parallel, we can write 'NO SOLUTION'

• Parallel lines have the SAME SLOPE but DIFFERENT y-intercepts

For lines to be right on top of one another...

• You should only see one line even though there are 2 equations.

• When this situation occurs, you can write "INFINITE SOLUTIONS"

• The 2 equations have to be mathematically the equal to one another for the lines to be on top of one another.

For lines to intersect once...

• The place where the line intersects is at an ordered pair

• Write the orderd pair in the form of (x,y).

• The slopes of the two lines must be different.

Solving Systems of Linear Equations by Substitution

Step #1 Isolate a variable in one of the equations to get an expression

Solving Systems

Steps #2 Substitute that expression (from step #1) into the other equation.

Solving Systems

Step #3 Solve for the intersection point (x , y).

Solving Systems

step #4 write your answer as an order pair (x, y).

***VERY IMPORTANT SLIDE***

SYSTEMS OF EQUATIONS ARE 2 EQUATIONS WITH 2 VARIABLES

One way to solve them is by ELIMINATING one of the variables

WHEN SOLVING USING ELIMINATION

• Look for opposite coefficients

• IF THERE IS NONE, MULTIPLY EVERY TERM IN AN EQUATION