Download presentation

Presentation is loading. Please wait.

Published byCorey Paul Modified over 7 years ago

1
3.1 System of Equations Solve by graphing

2
Ex 1) x + y = 3 5x – y = -27 Which one is the solution of this system? (1,2) or (-4,7) *Check (1,2)Check (-4,7) Is 1 + 2 ? 3Is -4 + 7 ? 3 3 = 3 yes 3 = 3 yes Is 5·1-2 ? -27 Is 5·(-4)-7 ? -27 5 - 2 ? -27 -20 – 7 ? -27 -3 = -27 no -27 = -27 yes So (1,2) is not the So (-4,7) is the solution Solutionof the system

3
Solve by Graphing Ex 1) y – x = 1 y + x = 3 y = x + 1 y = -x + 3 Therefore the solution of this system is (1,2) (1,2)

4
Solve by Graphing Ex 1) y = -3x + 5 y = -3x - 2 The lines are parallel, so there is no solution for this system of equations

5
Solve by Graphing Ex 1) 3y – 2x = 6 -12y + 8x = -24 3y = 2x + 6 -12y = -8x - 24 y = 2/3 x + 2 There are infinite numbers of solution because the lines are coinciding

6
A system of equations is consistent if they have at least one solution A system of equation is inconsistent if they have no solution A system of equations is dependent if it has many solutions A system of equations is independent if it has one solution or no solutions ***When an equation in a system can be obtained by multiplying both sides of another equation by a constant, the two equations are said to be dependent

7
Example Y = -2 X = 2 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: (2, -2), consistent, independent

8
Example 6x – 2y = 2 9x – 3y = 1 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: No solution; inconsistent, independent

9
Example Y = 3 - x 2x +2y = 6 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: Infinite many solutions; consistent, dependent

10
Example Y = 4 - x Y = x - 4 What is the solution? Dependent or independent? Consistent or Inconsistent? Answer: (4,0) consistent, independent

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google