7.1 graphing a linear system day 1
- 1. Chapter 7 Systems of Equations & Inequalities P. 424 Prerequisite Skills
- 2. • In this chapter, you will learn three different methods to solve a pair of linear equations simultaneously. • We will also learn the difference between solving an equation and solving an inequality.
- 3. • Section 7.1 Solve Linear Systems by Graphing (Graph & Check Method) • P. 427 This is the first of three method to solve a linear system.
- 4. Linear System: A system of linear equations (or simply a linear system) consists of two or more linear equations in the same variables. Example: x + 2y = 7 3x – 2y = 5
- 5. The solution of a system of linear equations in two variables is an ordered pair that satisfies each equation in the system.
- 6. EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1 3x – 2y = 5 Equation 2 SOLUTION The lines appear to intersect at the point (3, 2). CHECK Substitute 3 for x and 2 for y in each equation. x + 2y = 7 ? 3 + 2(2) = 7 7=7
- 7. EXAMPLE 1 Check the intersection point 3x – 2y = 5 ? 3(3) – 2(2) = 5 5=5 ANSWER Because the ordered pair (3, 2) is a solution of each equation, it is a solution of the system.
- 8. EXAMPLE 2 Use the graph-and-check method Solve the linear system: –x + y = –7 Equation 1 x + 4y = –8 Equation 2 SOLUTION STEP 1 Graph both equations.
- 9. EXAMPLE 2 Use the graph-and-check method STEP 2 Estimate the point of intersection. The two lines appear to intersect at (4, – 3). STEP 3 Check whether (4, –3) is a solution by substituting 4 for x and –3 for y in each of the original equations. Equation 1 Equation 2 –x + y = –7 x + 4y = –8 ? ? –(4) + (–3) = –7 4 + 4(–3) = –8 –7 = –7 –8 = –8
- 10. EXAMPLE 2 Use the graph-and-check method ANSWER Because (4, –3) is a solution of each equation, it is a solution of the linear system.
- 11. GUIDED PRACTICE graph-and-checkand 2 EXAMPLE 2 Use the for Examples 1 method Solve the linear system by graphing. Check your solution. 3. x – y = 5 3x + y = 3 ANSWER (2, 3)
- 12. • Assignment: P. 430- 431 Do # 1-5 orally together • Write out / graph 8-10, 12-14, 18-20 • Remember to CHECK your solution in both equations.