Review: Graphing an Equation X and Y Intercepts (plug in zeros) To find the y-intercept, let x=0 and solve for y. To find the x-intercept, let y=0 and solve for x. Plot both points (0, y) and (x, 0). Connect them with a line.

Graph 4x + 3y = 12 using intercepts Find x-intercept 4x + 3(0) = 12 Find y-intercept 4(0) + 3y = 12 4x = 12 3y = 12 x = 3 y = 4 Plot (3, 0) Plot (0, 4) Teach and demonstrate the concept.

Review: Graphing an Equation Slope-Intercept Form Write the equation in the form y = mx + b. Identify m and b. Plot the y-intercept (0, b). Starting at the y-intercept, find another point on the line using the slope. Draw the line through (0, b) and the point located using the slope.

Ex 3: Graph the line -2x + y = – 4. Write the equation in slope-intercept form. -2x + y = -4 +2x +2x x y We get the equation y = 2x – 4. So, m = 2 and b = - 4. 2. Plot the y-intercept, (0, - 4). (1, -2) 1 = rise run m = 2 2 3. The slope is 2. (0, - 4) 1 4. Start at the point (0, 4). Count 1 unit to the right and 2 units up to locate a second point on the line. The point (1, -2) is also on the line. 5. Draw the line through (0, 4) and (1, -2). Example: y=mx+b

What is a system of equations? A system of linear equations consists of two or more equations with the same variables. A solution of a linear system is the point that satisfies (or is a solution to) ALL of the equations. This point will be an ordered pair. When graphing, we will encounter three possibilities:

One Solution (Intersecting Lines) The point where the lines intersect is your solution. The solution of this graph is (1, 2) (1,2)

No Solution (Parallel Lines) These lines never intersect! Since the lines never cross, there is NO SOLUTION! Parallel lines have the same slope with different y-intercepts.

Infinitely Many Solutions (Coinciding Lines) These lines are the same! Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! Coinciding lines have the same slope and y-intercepts.

What is the solution of the system graphed below? (2, -2) (-2, 2) No solution Infinitely many solutions

Ex 1) Solve the linear system by graphing 2x + y = 4 x - y = 2 Graph both equations. We will graph using x- and y-intercepts (plug in zeros). Graph the ordered pairs. 2x + y = 4 (0, 4) and (2, 0) x – y = 2 (0, -2) and (2, 0)

Graph the equations. 2x + y = 4 (0, 4) and (2, 0) x - y = 2 Where do the lines intersect? (2, 0) 2x + y = 4 x – y = 2

Check your answer! To check your answer, plug the point back into both equations. 2x + y = 4 2(2) + (0) = 4 x - y = 2 (2) – (0) = 2

Ex 2) Solve the linear system by graphing y = 2x – 3 -2x + y = 1 Graph both equations. We will use slope- intercept form to graph. Make sure both equations are in slope-intercept form. y = 2x + 1

Notice that the slopes are the same with different y-intercepts. Graph the equations. y = 2x – 3 m = 2 and b = -3 y = 2x + 1 m = 2 and b = 1 Where do the lines intersect? No solution! Notice that the slopes are the same with different y-intercepts.

Check your answer! Not a lot to check…Just make sure you set up your equations correctly.

What is the solution of this system? 3x + y = -8 2y = -6x -16 (3, 1) (4, 4) No solution Infinitely many solutions

Solving a system of equations by graphing. There are 3 steps to solving a system using a graph. Graph using slope and y – intercept or x- and y-intercepts. Step 1: Graph both equations. This is the solution! LABEL the solution! Step 2: Do the graphs intersect? Substitute the x and y values into both equations to verify the point is a solution to both equations. Step 3: Check your solution.

Exit Ticket Solve the linear system by graphing: 1) y = 2x – 4 2) 2x – y = - 3 -4x + 2y = 6