swbat: solve systems of linear equations by graphing graph paper is preferred for these notes...
TRANSCRIPT
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SWBAT: solve systems of linear equations by graphing
GRAPH PAPER IS PREFERRED FOR THESE NOTES
Solving Systems by Graphing
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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.
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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.
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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
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New Vocabulary
System of linear equations: two or more linear equations together
Aka, 2 graphs of a line on the same grid.
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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.
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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
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You try: Solve by graphing. Check your solution.
Solve the system:y = x + 5Y = -4x
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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.
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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
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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)
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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.
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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
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Infinitely many solutions = same lineInfinitely many solutions = same line No Solution = parallelNo Solution = parallel
Review (past 2 slides)
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Sort your cards
Sort your cards into groups based on whether they have 1 solution, no solution, or infinitely many solutions
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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.