SWBAT: solve systems of linear equations by graphing

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Solving Systems by Graphing

Why learn this?

To solve problems by comparing costs for services like television.

Write your reason for learning this at the top of your notes. When you are finished, put your pencils down.

Review: Graphing in Slope-intercept Form

Slope intercept: y = mx + b X, Y are coordinates of the line B is the y-intercept (0, b) M is the slope

Slope describes how a line looks:

Graphing slope-intercept: 3x + 2 = y Find the y-intercept: (0, 2) Move by the slope: up 3, over 1.

New Vocabulary

Solution of a linear equation: all the pairs of x,y values that land on a line.

Example: (0, 2) is a solution of

the equation.(4,0) is a solution of

the equation(-4, 4) is a solution

New Vocabulary

System of linear equations: two or more linear equations together

Aka, 2 graphs of a line on the same grid.

New Vocabulary

Solution of the system: any ordered pair that is shared between two equations.

Example: the point (1,3) is a solution of the system.

Solve the system of linear equations by graphing

Step 1: graph line 1Step 2: graph line 2Find the point of

intersection (you will need to have drawn a good graph!)

Check the point by filling it back into both equations.

Example: Y = 2x – 3Y = x – 1

Check, is (2, 1) a solution to both?

✔1 = 2(2) – 3? Yes, solution checks for eqn. 1

1 = (2) – 1? Yes, solution checks for eqn. 2

Checks for both. It is the solution

You try: Solve by graphing. Check your solution.

Solve the system:y = x + 5Y = -4x

You try: Solve by graphing. ANSWER

Solve the system:y = x + 5Y = -4x

✔4 = (-1) + 5 Yes. 4 = -4(-1) Yes. Yes, this point is a

solution for both lines.

Solve by Graphing. Verify your answer.

1) y = -2/3x + 1 y = 3/2x – 1

2) Y = 4x + 5 Y = 2x – 1

3) Y = 2.5x – 3 Y = x

4) 7x – 3 = y 3x + 1 = y

5) 5x – 2 = y 2x + 1 = y

6) 4x = y 6x – 3 = y

Solve by Graphing. Verify your answer.

1) y = -2/3x + 1 y = 3/2x – 1(12/13, 5/13)2) Y = 4x + 5 Y = 2x – 1( -3, -7)3) Y = 2.5x – 3 Y = x(2, 2)

4) 7x – 3 = y 3x + 1 = y(1, 4)5) 5x – 2 = y 2x + 1 = y(1, 3)6) 4x = y 6x – 3 = y(3/2, 6)

Think logically:

Are there any lines that do not intersect?Parallel lines

What does solution mean again?Where 2 lines intersect

Is there going to be a solution for lines that do not intersect?

No. When lines are parallel, there is no solution.

Think logically:

Is there more than one way to represent the equation of the same line?

Yes, slope-intercept form and Ax + By = C form.

How many times does the same line intersect with itself?

Infinitely many.

How many solutions will there be for the equation of the same line?

Infinitely many

Infinitely many solutions = same lineInfinitely many solutions = same line No Solution = parallelNo Solution = parallel

Review (past 2 slides)

Sort your cards

Sort your cards into groups based on whether they have 1 solution, no solution, or infinitely many solutions

Practice

Complete Pg. 272 #1 – 45 odds onlyIt will be collected at the end of the hour for

a gradeIf you finish early, complete the exit ticket

and pick up the homework.