This document provides steps to solve the simultaneous equations y = 2x + 1 and y = 4 - x graphically. It involves constructing tables of values for each equation, plotting the equations on a graph, and finding the point where the lines intersect. The solution is where x = 1 and y = 3.

1. Solving simultaneous
equations graphically

2. y = 2x + 1
y = 4 - x
Solve the simultaneous equations.
The Question:

3. Solution (by Elimination)
y = 2x + 1
y = 4 – x
y = 2x + 1
y = -x + 4
y = 2x + 1
2y = -2x + 8 (x2)
3y = 9
y = 3
x = 4 – y = 4 – 3 = 1
Solution: x = 1, y = 3
Substitute y to find the value of x

4. y = 2x + 1
y = 4 - x
Solve the simultaneous equations graphically.
The Question:

5. y = 2x + 1 y = 4 - x
Begin by constructing a table of values:
x
y
y = 2x + 1
-2 0 2 4
Use the equation to fill in the y value when x = -2
-3
Now fill in the rest of the table
1 5 9

6. y = 2x + 1 y = 4 - x
x
y
-2
-3
0
1
2
5
4
9
y = 2x + 1
Use the
table to draw
the graph of
the equation.
-4
-2
0
2
4
6
8
10
-3 -2 -1 0 1 2 3 4 5
x
y
y = 2x + 1

7. y = 2x + 1 y = 4 - x
Now construct a second table of values:
6 4 2
x
y
-2 0 2 4
0
Y = 4 - x
Plot this line on the axes you used earlier...

8. -4
-2
0
2
4
6
8
10
-3 -2 -1 0 1 2 3 4 5
x
y
y = 2x + 1
y = 4 - x
The solution is where the 2 lines cross:
Read the x-value from the x-axis... 1
Now read off the y-value... 3

9. So the solution of y = 2x + 1 and
y = 4 - x is...
x = 1 y = 3and

10. So the solution of y = 2x + 1 and
y = 4 - x is...
x = 1 y = 3and