The solution of a linear equation: - We say that x=m, y=n is a solution of ax+by+c=0.
How to solve linear equations by graphing: -
i) Express y in terms of x.
ii) Choose at least two convenient values of x and find the corresponding values of y, satisfying the given equation.
iii) Write down these values of x and y in the form of a table.
iv) Plot the order pairs (x, y) from the table on a graph paper.
v) Join these points by a straight line and extend it in both the directions.
This line is the graph of the equation a x + b y + c = 0.
Example: - Draw the graph of the equation 2 x – y + 3. Using the graph, find the value of y, when x = - 2.
Solution: - 2 x – y + 3 = 0 implies y = 2 x + 3
When x = 0, then y = 2 * 0 + 3 = 3
When x = 1, then y = 2 * 1 + 3 = 5
Now, plot the points A (0, 3) and B (1, 5) on a graph paper.
Join AB and extend it in both directions.
Then, the line AB is the required graph of 2 x – y + 3 = 0.
Given: x = -2. Take a point M on the x-axis such that OM=-2.
Draw MP, parallel to the y-axis, cutting the line AB at P.
Therefore x = -2, then y = -1