1. WARM UP LINEAR EQUATIONS Solve the equation (Lesson 3.1, 3.4) 1.5(2x + 4) = 2(10 + 5x) 2.2x + 6(x + 1) = -2 3

2. WARM UP LINEAR EQUATIONS Solve the equation (Lesson 3.1, 3.4) 1.5(2x + 4) = 2(10 + 5x) 2.2x + 6(x + 1) = -2 2

3. WARM UP LINEAR EQUATIONS Solve the equation (Lesson 3.1, 3.4) 1.5(2x + 4) = 2(10 + 5x) 2.2x + 6(x + 1) = -2 1

4. LINEAR EQUATIONS Solve the equation (Lesson 3.1, 3.4) 1.5(2x + 4) = 2(10 + 5x) 2.2x + 6(x + 1) = -2 WARM UP 0

5. 7.1 Graphing Linear SystemsGOAL Estimate the solution of a system of linear equations by graphing KEY WORDS System of linear equations Solution of a linear system Point of intersection

6. 7.1 Graphing Linear Systems EXAMPLE 1 EXAMPLE 1 FIND THE POINT OF INTERSECTION Use the graph to estimate the solution of the linear system. Then Check your solution algebraically. 3x + 2y = 4 -x + 3y = -5 3x + 2y = 4

7. 7.1 Graphing Linear Systems EXAMPLE 1 EXAMPLE 1 FIND THE POINT OF INTERSECTION Use the graph to estimate the solution of the linear system. Then Check your solution algebraically. SOLUTION The lines appear to intersect At the point (2, -1) -x + 3y = -5 3x + 2y = 4 (2, -1)

8. 7.1 Graphing Linear Systems EXAMPLE 1 EXAMPLE 1 FIND THE POINT OF INTERSECTION Use the graph to estimate the solution of the linear system. Then Check your solution algebraically. CHECK Substitute 2 for x and -1 for y in each equation -x + 3y = -5 3x + 2y = 4 (2, -1)

9. 7.1 Graphing Linear Systems EXAMPLE 1 EXAMPLE 1 FIND THE POINT OF INTERSECTION Use the graph to estimate the solution of the linear system. Then Check your solution algebraically. ANSWER> Because (2, -1) makes each equation true, (2, -1) the solution of the system of Linear equations. -x + 3y = -5 3x + 2y = 4 (2, -1)

10. 7.1 Graphing Linear Systems SOLVING A LINEAR SYSTEM USING GRAPH-AND-CHECK ①WRITE each equation in slope-intercept form. ②GRAPH both equations in the same coordinate plane. ③ESTIMATE the coordinates of the point of intersection. ④CHECK whether the coordinates give a solution by substituting them into each equation of the original linear system.

11. 7.1 Graphing Linear Systems GRAPH-AND-CHECK to solve the linear system. 1.x + y = 4 2x + y = 5 2.x – y = -2 x + y = -4 CHECK POINT CERTIFIED

12. 7.1 Graphing Linear Systems Page 392-393 #7 - 24 Graph 16 - 24 CLASSWORK