Graph Of Linear Equation
This video course helps students learn how to solve simultaneous equations using graphs. Through clear examples, students will practise drawing two straight lines accurately by plotting points and choosing suitable scales. They will also learn how the point where the lines intersect gives the solution to both equations.
Related Lessons:
Example 1: Solving Simultaneous Equations Mathematically
In this first video, we will recap how to solve simultaneous equation using mathematical method.
Solve the simultaneous equation \(y=-\ \frac{3}{2}x-1\) and \(y=\frac{1}{2}x+1\) by using simultaneous equation.
Solution:
\(y=-\ \frac{3}{2}x-1\)……(1)
\(y=\frac{1}{2}x+1\)……(2)
Sub (1) into (2):
\(-\ \frac{3}{2}x-1=\frac{1}{2}x+1\)
\(x=-2\)
Sub \(x=-2\) into (1):
\(y=\ \frac{1}{2}\)
Therefore, \(x=-2,\ y=\ \frac{1}{2}\)
Example 1: Solving Simultaneous Equations Graphically
For the same example, we will learn how to solve simultaneous equations graphically by plotting two straight lines.
We are going to go through the technique by solving the equation \(y=-\ \frac{3}{2}x-1\) and \(y=\frac{1}{2}x+1\) graphically.
The steps are as follow:
- Select 3 \(x\)-values as far apart as possible. In this case, we select \(x=-2\), 0 and 2
- Next, we will calculate the corresponding y value for the corresponding \(x\) value to get 3 coordinate pairs for each equation.
- By plotting the points on the graph paper, we will get 2 straight lines.
- The intersection of the 2 straight lines will be the graphical solution. In this example, the intersection point is \((-2, \frac{1}{2})\)
Example 2
Solve the simultaneous equation \(2𝑥+𝑦=6\) and \(𝑦=𝑥\) graphically.
Example 3
Solve the simultaneous equation \(𝑦=-𝑥+3\) and \(𝑦=2𝑥-3\) graphically.
Example 4
Solve the simultaneous equation \(𝑦=𝑥+1\) and \(𝑦=-𝑥+3\) graphically.