Linear EquationsSolving Systems by Graphing

Lesson 23

1. Is (4, 1) on the line y = 2x − 5?

2. Is (0, −5) on the line 4x + 2y = 10?

3. Is (−2, 7) on the line y = 3(x + 5) – 2?

Warm-Up

Solving Systems by Graphing

Target: Determine the solution to a system

of equations by graphing.

Sue graphed the following system. She listed her solution to the system below. Decide whether her ordered pair is a solution to the system of equations.

Sue’s Answer: (−4, 3)−2x + 4y = 20 3x + y = −9−2(−4) + 4(3) 20 ≟ 3(−4) + (3) −9≟8 + 12 20 ≟ −12 + 3 −9≟20 = 20 −9 = −9 Yes, it is the solution!

Example 1a

Sue graphed the following system. She listed her solution to the system below. Decide whether her ordered pair is a solution to the system of equations.

Sue’s Answer: (−9, 0)y = x + 3 x + y = 9

0 (−9) + 3 ≟ −9 + 0 9≟0 −3 + 3≟0 = 0 −9 ≠ 9 No, not the solution.

Example 1b

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1. Convert both linear equations in the system to slope-intercept form.

2. Graph both equations on the same coordinate plane. Be sure to clearly mark at least three points on each line.

3. Determine the point of intersection.

4. Verify that the ordered pair is the solution by substituting the x- and y-values into each equation in the system.

Solving Systems of Linear Equations by Graphing

Steps to graph using the graphing calculator. 1. Press the “Y=“ button2. Type in the equation using “Alpha, Y=, 1” for

fractions, and “X,T,O,n” for the X3. Press the “graph” button4. Press “2nd, TRACE, 5” to find the Y-intercept5. To Find the intersection of system: graph both

equations then select “2nd, TRACE, 5” Then hit enter 3 times and it will give you the point of intersection of the two lines.

Slope-Intercept Form of a Linear Equation

Solve the system of equations by graphing. Check the solution.

y = x – 3 and 3x + 2y = 2 – 3x – 3x

2y = 2 – 3x 2 2 y = 1 – x

Intersection: (2, –2)

Example 2

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Solve the system of equations by graphing. Check the solution.

Check the solution of (2, –2).

y = x – 3 and 3x + 2y = 2

–2 = (2) – 3 3(2) + 2(–2) = 2–2 = 1 – 3 6 + –4 = 2–2 = –2 2 = 2

Example 2 (continued)

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Solve the system of equations by graphing.

y = x + 4

y = – x + 7

Exit Problems

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Why is it important, when graphing, to find more than two points on a line before drawing a line through the points?

Communication Prompt