The document focuses on solving simultaneous equations graphically, providing multiple examples and methods for demonstrating this technique. It includes instructions for sketching equations, identifying gradients and y-intercepts, as well as examples of finding solutions at the intersection points of the graphs. Various equations and their corresponding solutions are presented to illustrate the process.

1. LO: To be able to solve simultaneous equations graphically
Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. LO: To be able to solve simultaneous equations graphically
Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
We are learning to solve
simultaneous equations
graphically.

4. Tuesday, 02 July 2024 Simultaneous Equations Graphically
9x – 8y = -36
x + 2y = 6 (1)
(2)
Taking eq (1)
x + 2y = 6
x
y
0
3
6
0
Taking eq (2)
9x – 8y = -36
x
y
0
4.5
-4
0
Eg 1
x + 2y = 6
9x – 8y = -36
x = -1, y = 3.5

5. Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
Method 2

7. Tuesday, 02 July 2024 Simultaneous Equations Graphically
y = mx + 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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
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. Tuesday, 02 July 2024 Simultaneous Equations Graphically
Starter (extended version)

15. Tuesday, 02 July 2024 Simultaneous Equations Graphically
Starter: Copy and complete the following table:
Equation Gradient y – intercept
y = 3x + 2
2 7
y = 3x 3
y = -4x + 5
½ 4
2y = 4x + 6

16. Tuesday, 02 July 2024 Simultaneous Equations Graphically
Starter: Copy and complete the following table:
Equation Gradient y – intercept
y = 3x + 2 3 2
y = 2x + 7 2 7
y = 3x 3 0
y = -4x + 5 -4 5
y = ½x + 4 ½ 4
2y = 4x + 6 2 3