12-7 Solving systems of linear equations by graphing
12-7 SOLVING SYSTEMS OF LINEAR EQUATIONS BY GRAPHING MATH 8 MR. DIXON
Additional Example 1: Graphing a System of Linear Equations by Graphing A fishing boat leaves the harbor traveling east at 16 knots (nautical miles per hour). After it travels 40 nautical miles, a Coast Guard cutter follows the boat, traveling at 26 knots. After how many hours will the Coast Guard Cutter catch up with the fishing boat? Let t = time in hours Let d = distance in nautical miles Fishing boat distance: d = 16t + 40 Coast Guard cutter distance: d = 26t
Additional Example 1 Continued Graph each equation. The point of intersection appears to be (4, 104). Check d = 16t + 40 ?
104 = 16(4) + 40 104 = 104 d = 26t ? 104 = 26(4) 104 = 104 The Coast Guard cutter will catch up after 4 hours, 104 nautical miles from the harbor.
Check It Out: Example 2 A bus leaves the school traveling west at 50 miles per hour. After it travels 15 miles, a car follows the bus, traveling at 55 miles per hour. After how many hours will the car catch up with the bus?
Let t = time in hours Let d = distance in miles bus distance: d = 50t + 15 car distance: d = 55t
Check It Out: Example 2 Continued Graph each equation. The point of intersection appears to be (3, 165). Check d = 50t + 15
165 = 50(3) + 15 165 = 165 d = 55t ? 165 = 55(3)
Distance (mi)
?
200
150 100 50 1 2 3 4 5 6 7 8 9 10 Time (h)
165 = 165 The car will catch up after 3 hours, 165 miles from the school.
Additional Example 3: Solving Systems of Linear Equations by Graphing y = 2x – 7 3x + y = 3 Step 1: Solve both equations for y. y = 2x – 7
3x + y = 3 –3x –3x y = 3 – 3x
Step 2: Graph. The lines intersect at (2, –3), so the solution is (2, –3).
Additional Example 3 Continued Check y = 2x – 7 ? –3 = 2(2) – 7 ?
–3 = –3
3x + y = 3 ? 3(2) + (–3) = 3 ?
3=3
Additional Example 4: Solving Systems of Linear Equations by Graphing 2x + y = 9 y – 9 = –2x Step 1: Solve both equations for y. 2x + y = 9 –2x –2x y = –2x + 9
y – 9 = –2x +9 +9 y = –2x + 9
Step 2: Graph. The lines are the same, so the system has infinitely many solutions.
Additional Example 4 Continued Check ?
y=y ? –2x + 9 = –2x + 9 +2x +2x ?
9=9
ASSIGNMENT • PRACTICE A & B WORKSHEET • USE RULER TO CREATE STRAIGHT LINES.
Additional Example 1: Graphing a System of Linear Equations by Graphing A fishing boat leaves the harbor traveling east at 16 knots (nautical miles per hour). After it travels 40 nautical miles, a Coast Guard cutter follows the boat, traveling at 26 knots. After how many hours will the Coast Guard Cutter catch up with the fishing boat? Let t = time in hours Let d = distance in nautical miles Fishing boat distance: d = 16t + 40 Coast Guard cutter distance: d = 26t
Additional Example 1 Continued Graph each equation. The point of intersection appears to be (4, 104). Check d = 16t + 40 ?
104 = 16(4) + 40 104 = 104 d = 26t ? 104 = 26(4) 104 = 104 The Coast Guard cutter will catch up after 4 hours, 104 nautical miles from the harbor.
Check It Out: Example 2 A bus leaves the school traveling west at 50 miles per hour. After it travels 15 miles, a car follows the bus, traveling at 55 miles per hour. After how many hours will the car catch up with the bus?
Let t = time in hours Let d = distance in miles bus distance: d = 50t + 15 car distance: d = 55t
Check It Out: Example 2 Continued Graph each equation. The point of intersection appears to be (3, 165). Check d = 50t + 15
165 = 50(3) + 15 165 = 165 d = 55t ? 165 = 55(3)
Distance (mi)
?
200
150 100 50 1 2 3 4 5 6 7 8 9 10 Time (h)
165 = 165 The car will catch up after 3 hours, 165 miles from the school.
Additional Example 3: Solving Systems of Linear Equations by Graphing y = 2x – 7 3x + y = 3 Step 1: Solve both equations for y. y = 2x – 7
3x + y = 3 –3x –3x y = 3 – 3x
Step 2: Graph. The lines intersect at (2, –3), so the solution is (2, –3).
Additional Example 3 Continued Check y = 2x – 7 ? –3 = 2(2) – 7 ?
–3 = –3
3x + y = 3 ? 3(2) + (–3) = 3 ?
3=3
Additional Example 4: Solving Systems of Linear Equations by Graphing 2x + y = 9 y – 9 = –2x Step 1: Solve both equations for y. 2x + y = 9 –2x –2x y = –2x + 9
y – 9 = –2x +9 +9 y = –2x + 9
Step 2: Graph. The lines are the same, so the system has infinitely many solutions.
Additional Example 4 Continued Check ?
y=y ? –2x + 9 = –2x + 9 +2x +2x ?
9=9
ASSIGNMENT • PRACTICE A & B WORKSHEET • USE RULER TO CREATE STRAIGHT LINES.
