Solving simultaneous

equations graphically

y = 2x + 1y = 4 - x

Solve the simultaneous equations.

The Question:

Solution (by Elimination)

y = 2x + 1y = 4 – xy = 2x + 1y = -x + 4y = 2x + 12y = -2x + 8 (x2)3y = 9y = 3

x = 4 – y = 4 – 3 = 1

Solution: x = 1, y = 3

Substitute y to find the value of x

y = 2x + 1y = 4 - x

Solve the simultaneous equations graphically.

The Question:

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

y = 2x + 1 y = 4 - x

x

y-2

-3

0

1

2

5

4

9

y = 2x + 1Use 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 5x

y

y = 2x + 1

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...

-4

-2

0

2

4

6

8

10

-3 -2 -1 0 1 2 3 4 5x

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

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

x = 1 y = 3 and