Simultaneous-Equations-Graphicallby.pptx

Simultaneous-Equations-Graphicallby

1. Starter: Copy and complete the following table: Equation Value of x Value of y y = 3x + 2 2 y = 3x 3 y = -4x + 5 -1 2y = 4x + 6 -3

2. Starter: Copy and complete the following table: Equation Value of x Value of y y = 3x + 2 2 8 y = 3x 1 3 y = -4x + 5 -1 10 2y = 4x + 6 -3 -3

3. We are learning to solve simultaneous equations graphically.

4. 9x – 8y = -36 x + 2y = 6 (1) (2) Taking eq (1) x + 2y = 6 x y 3 6 Taking eq (2) 9x – 8y = -36 x y 4.5 -4 Eg 1 x + 2y = 6 9x – 8y = -36 x = -1, y = 3.5

5. a) y = 3x - 7 b) y = x - 3 y = x – 1 y = 2x – 7   c) y = x + 2 d) y = 2x + 6 x + 2y = 4 x + y = 0   e) x + y = -6 f) y = 0.5x – 2.5 x – y = -2 x + y = 5 g) 2x + y = -7 h) y = 3x + 2 x + y = -6 y = -1 + 3x   x = 3 y = 2 x = 4, y = 1 x = 0, y = 2 x = -2, y = 2 x = -4, y = -2 x = 5, y = 0 x = -1, y = -5 NO SOLUTIONS!!!

6. Method 2

7. y = m x + c m is the gradient, or the slope of the graph c is the y-intercept, or where the graph cuts the y-axis Remember:

8. Solve the simultaneous equations y = 2x + 1 and y = 3 graphically: Start by sketching y = 2x + 1 Start at 1 on the y-axis. For every 1 across, go up 2. Join with a straight line.

9. Solve the simultaneous equations y = 2x + 1 and y = 3 graphically: Now sketch y = 3. This means that for every value of x, y = 3. Find 3 on the y axis and draw a horizontal line through it.

10. Solve the simultaneous equations y = 2x + 1 and y = 3 graphically: The solution is the coordinate where the graphs cross. (1, 3) So, x = 1 and y = 3

11. Solve the simultaneous equations y = 3x + 2 and y = 6 – x graphically: Start by sketching y = 3x + 2 Start at 2 on the y-axis. For every 1 across, go up 3. Join with a straight line.

12. Solve the simultaneous equations y = 3x + 2 and y = 6 – x graphically: Now sketch y = 6 – x. Start at 6 on the y-axis. For every 1 across, go down 1. Join with a straight line.

13. Solve the simultaneous equations y = 3x + 2 and y = 6 – x graphically: The solution is the coordinate where the graphs cross. (1, 5) So, x = 1 and y = 5

14. Starter (extended version)

15. Starter: Copy and complete the following table: Equation Gradient y – in tercept y = 3x + 2 2 7 y = 3x 3 y = -4x + 5 ½ 4 2y = 4x + 6

16. Starter: Copy and complete the following table: Equation Gradient y – in tercept y = 3x + 2 3 2 y = 2x + 7 2 7 y = 3x 3 y = -4x + 5 -4 5 y = ½x + 4 ½ 4 2y = 4x + 6 2 3