2. Algebra Unit 4 Graphing Systems of Equations Turn to page 27 in packet

3. Math Dude Video (5:40) Watch video and be ready to answer questions afterwards. 1. There were two methods of graphing mentioned in the video. What were they? 2. Equations can be written in slope-intercept form and standard form. Which method of graphing should you use for each form? Slope-intercept form: _______________________ Standard form: _____________________________ 3. Where on the graph is the solution of the system of equations?

5. Questions about video 1. There were two methods of graphing mentioned in the video. What were they? Intercepts Slope & y-intercept 2. Equations can be written in slope-intercept form and standard form. Which method of graphing should you use for each form? Slope-intercept form: _______________________ Standard form: _____________________________ Slope & y-intercept Intercepts 3. Where on the graph is the solution of the system of equations? The solution is the point where the lines cross. 2:001:591:581:571:561:551:541:531:521:511:501:491:481:471:461:451:441:431:421:411:401:391:381:371:361:351:341:331:321:311:301:291:281:271:261:251:241:231:221:211:201:191:181:171:161:151:141:131:121:111:101:091:081:071:061:051:041:031:021:011:000:590:580:570:560:550:540:530:520:510:500:490:480:470:460:450:440:430:420:410:400:390:380:370:360:350:340:330:320:310:300:290:280:270:260:250:240:230:220:210:200:190:180:170:160:150:140:130:120:110:100:090:080:070:060:050:040:030:020:01End2:00 End123456789101112131415161718192021222324252627282930

6. Defining a System of Equations A grouping of 2 or more equations, containing one or more variables. x + y = 2 2x + y = 5 2y = x + 2 y = 5x - 7 6x - y = 5

7. STEPS TO SOLVING A SYSTEM OF EQUATIONS BY GRAPHING 1.GRAPH BOTH EQUATIONS USING EITHER: – X & Y-INTERCEPTS – SLOPE-INTERCEPT FORM 2. FIND THE SOLUTION: ORDERED PAIR WHERE THE TWO LINES INTERSECT. WRITE ANSWER AS A COORDINATE. You can check the solution by plugging the coordinate back into both equations

8. (A) y = x + 1 (B) y = 3 (2, 3) m = 1, b = 1 (0, 3) (2, 3) EXAMPLE 1: SOLVE THE SYSTEM OF EQUATIONS BY GRAPHING (A) y = x +1 (B) y = 3 STEP 1: Graph both equations STEP 2: Find intersection point

9. Check: Check to make sure the solution works for both equations (3) = (2) + 1 3 = 3 (A) y = x + 1 (B) y = 3 (2, 3) 3 = 3 Yes, (2,3) is the solution of the system of equation. (2,3) is the point where the lines intersect.

10. Guided Practice Complete examples 2 and 3 with your group. 10 minutes End

11. (A) x + y = 2 (B) 2x + y = 5 Example 2 STEP 1: Graph both equations Use using intercepts (A) x + y = 2(B) 2x + y = 5 Solve the system of equations by graphing

12. (A) x + y = 2 STEP 1: continued (B) 2x + y = 5 (3, -1) (0, 2) & (2, 0) (0, 5) & (2.5, 0) Example 2 STEP 2: Find intersection point

13. STEP 3: Check to make sure the solution works for both equations (-1) = -(3) + 2 -1 = -2(3) + 5 -1 = -6 + 5 (3, -1) -1 = -1 (A) y = -x + 2(B) y = -2x + 5 Example 2 Yes, (3,-1) is the solution of the system of equation. (3,-1) is the point where the lines intersect.

14. (A) x = -2 y = -x + 3 Example 3 (B) x + y = 3 STEP 1: Graph both equations Put both equations in “y=mx+b” form -x

15. (A) x = -2 STEP 1: continued (B) y = -x + 3 (-2, 5) Vertical line @ -2 on the x-axis m = -1, b = 3 Example 3 STEP 2: Find intersection point

16. (A) x = 2 STEP 1: Graph each line (B) y = 3 (2, 3) Vertical line @ 2 on the x-axis Horizontal line @ 3 on y-axis Example 3 STEP 2: Find intersection point (A) x = 2(B) y = 3

17. STEP 3: Check to make sure the solution works for both equations (2) = 2 3 = 3 (2, 3) 3 = 3 (A) x = 2(B) y = 3 Example 3 Yes, (2,3) is the solution of the system of equation. (2,3) is the point where the lines intersect.

18. iPad Practice Clear the cookies in Safari Go to www.ixl.comwww.ixl.com Click on Algebra 1 then on U2 and do three problems each. Then click on U4 and do two problems each. OR, scan the QR codes below. U2U4 10 minutes

19. Ticket out the door Complete the problem by yourself. Put the paper in the basket on the way out the door. Homework Pages 28-29 in packet

20. STEP 3: Check to make sure the solution works for both equations (-2) = -2 5 = -(-2) + 3 5 = 2 + 3 (-2, 5) 5 = 5 (A) x = -2(B) y = -x + 3 Example 4 – TRY ON YOUR OWN!