SECTION 7 1 Solving Linear Systems by Graphing

SECTION 7. 1 Solving Linear Systems by Graphing WHAT’S IMPORTANT: -- Be able to solve a system of linear equations by graphing. -- Be able to model a real-life problem using a linear system.

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Write a linear equation in slope intercept form for the cost of the following: 1. What is the slope? or

Write a linear equation in slope intercept form for the cost of the following: 1. or 2. or

Write a linear equation in slope intercept form for the cost of the following, then graph the equation: 1. or 2. or

Emma wants to purchase DVDs to add to her collection. Through Barnes and Noble the DVDs cost $4. 00 each plus $6. 00 to ship them. Amazon sells the same DVDs for $5 each and only charges $3. 00 to ship them. At what point do the two companies charge the same amount for the DVDs? Solve by graphing:

7. 1: “Solving Linear Systems by Graphing” l

l No Solution

7. 1: “Solving Linear Systems by Graphing” l Example: Check whether (1, 4) is a solution to the following system: x – 3 y = -5 -2 x + 3 y = 10 l In both equations, put 1 in for x and 4 in for y and see if they check out.

7. 1: “Solving Linear Systems by Graphing” l Example: Check whether (1, 4) is a solution to the following system: x – 3 y = -5 1 – 3(4) = -5 1 – 12 = -5 -11 = -5 l Since -11 -5, the point (1, 4) is NOT a solution to the system. We do not even have to check the other equation.

7. 1: “Solving Linear Systems by Graphing” l

7. 1: “Solving Linear Systems by Graphing” l Example: Check whether (-5, 0) is a solution to the following system: l x – 3 y = -5 -2 x + 3 y = 10 l -5 – 3(0) = -5 -2(-5) + 3(0) = 10 l -5 – 0 = -5 10 + 0 = 10 l -5 = -5 10 = 10 l Since this ordered pair checks out true in both equations, (-5, 0) IS a solution to the system.

7. 1: “Solving Linear Systems by Graphing” l Example: Solve the following system by graphing: 2 x – 2 y = -8 2 x + 2 y = 4 l In both equations, I am going to put the equations in slope-intercept form to help me construct the graph.

7. 1: “Solving Linear Systems by Graphing” 2 x – 2 y = - 8 -2 x – 2 y = -2 x - 8 -2 -2 -2 y = 1 x + 4 2 x + 2 y = 4 -2 x 2 y = -2 x + 4 2 2 2 y = -1 x + 2

7. 1: “Solving Linear Systems by Graphing” Now, plot the points and draw the lines. y=x+4 y = -x + 2

7. 1: “Solving Linear Systems by Graphing” l These lines appear to cross at (-1, 3).

7. 1: “Solving Linear Systems by Graphing” l l l Check the ordered pair in both equations (-1, 3). 2(-1) – 2(3) = -8 2(-1) + 2(3) = 4 -2 – 6 = -8 -2 + 6 = 4 -8 = -8 4=4 The ordered pair (-1, 3) checks out, so it IS a solution.

7. 1: “Solving Linear Systems by Graphing” l If your graph of the system is a pair of lines that intersect at one point (as below), then the system has exactly one solution. l Our one solution was (-1, 3)

7. 1: “Solving Linear Systems by Graphing” l