Solving simultaneous equations graphically
Simultaneous equations can be solved algebraically or graphically. Knowledge of plotting linear equations is needed to solve equations graphically.
To find solutions from graphs, look for the point where the two graphs cross one another. This is the solution point. For example, the solution for the graphs \(y = x + 1\) and \(x + y = 3\) is the coordinate point (1, 2).
The solution to these equations is \(x = 1\) and \(y = 2\).
Example
Solve the simultaneous equations \(x + y = 5\) and \(y = x + 1\) using graphs.
To solve this question, first construct a set of axes, making sure there is enough room to plot the two graphs.
Now draw the graphs for \(x + y = 5\) and \(y = x + 1\).
To draw these graphs, use a table of values:
\(y = x + 1\)
| \(x\) | -1 | 0 | 1 | 2 | 3 |
| \(y\) | 0 | 1 | 2 | 3 | 4 |
| \(x\) |
|---|
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |
| \(y\) |
|---|
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
\(x + y = 5\)
| \(x\) | -1 | 0 | 1 | 2 | 3 |
| \(y\) | 6 | 5 | 4 | 3 | 2 |
| \(x\) |
|---|
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |
| \(y\) |
|---|
| 6 |
| 5 |
| 4 |
| 3 |
| 2 |
Plot these graphs onto the axes and label each graph.
The point of intersection is (2, 3) which means \(x = 2\) and \(y = 3\).
More guides on this topic
- Expansion of brackets
- Factorising an algebraic expression
- Completing the square in a quadratic expression
- Simplifying algebraic fractions
- Applying the four operations to algebraic fractions
- Determining the equation of a straight line
- Working with linear equations and inequations
- Changing the subject of a formula
- Determine the equation of a quadratic function from its graph
- Sketching a quadratic function
- Identifying features of a quadratic function
- Solving a quadratic equation
- Solving a quadratic equation using the quadratic formula
- Using the discriminant to determine the number of roots
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