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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

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.

When x = 0, then y = 2 * 0 + 3 = 3

When x = 1, then y = 2 * 1 + 3 = 5

X | 0 | 1 |

Y | 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.

Clearly PM=-1.

Therefore x = -2, then y = -1