Simultaneous Equations Graphically
Wackford Squeers 1
Simultaneous Equations 1 By now you should be able to solve simultaneous equations by elimination – if you are unsure, look at the booklet called
Simultaneous Equations – By Elimination. We will solve two equations graphically and then solve them by elimination – to see if we are right! Solve the equations:
y = 2x + 16 y=4-x The first thing to notice is that these two equations are both LINEAR – that is to say their graphs will be straight line The second thing to comment on is the fact that the solution to the problem will be where the two graphs cross Finally, we can see, by looking at the equations, that one line slopes from bottom left to top right (y = 2x + 1) and the other slopes form top left to bottom right (y = 4 – x). First thing first – we will create the tables which we will use to plot the points x Y = 2x + 16
-3 10
-2 12
-1 14
0 16
1 18
2 20
3 22
x Y=4-x
-3 7
-2 6
-1 5
0 4
1 3
2 2
3 1
So we have values for x from -3 to +3 And values for y from 1 to 22 (looking at BOTH tables)
2
. . . . . . .. ... ..
y = 2x + 16
We now draw the axes and plot the points:
22 20 18 16
The solution is (-4,8)
14 12 10
y=4-x
8 6 4
2
-4
-3
-2
-1
0
1
2
3
4
Exercises for You 1 For the equations:
y = 2x – 5 y = 3 – 2x Complete the tables below x y = 2x – 5
-2 -9
-1
0 -5
1
2
x y = 3 – 2x
-2 7
-1
0 3
1
2
3
On a grid similar to the one below draw the graphs and hence solve the simultaneous equations
12 0 8 6 4 2 -4
-3
-2
-1
0
10
1
2
3
4
-2 -4 -6 -8 -10
Exercises for You For the equations:
y=x–2 y = 3x + 4 Draw the appropriate tables of values for each equations Draw an appropriate grid and axes and plot the points from the table Solve the simultaneous equations
4