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Graph of Linear Equation in Two Variables

When we draw the graph of the equation ax + by + c = 0, we get a straight line.

 

 

Note: The graph of a first degree equation in one or two variables is a (straight) line. Because of this reason we call it a linear equation.



Draw the graph of y = 2x - 1. Use it to find some solutions of the equation. Check from the graph whether x = -1, y = -3 is the solution.
y = 2x – 1
If x = 0; y = 2 × 0 - 1 = 0 - 1= -1
If x = 1; y = 2 × 1 - 1 = 2 - 1 = 1
If x = 2; y = 2 × 2 – 1 = 4 - 1 = 3

We thus have the following points:


 
 

x

0

1

2

y

-1

1

3


Plotting A (0, -1), B (1, 1), C (2, 3), we draw the graph.

We see that the point P (-1, -3) lies on the line, which shows that x = -1 and y = -3 is a solution of the equation y = 2x - 1. Q(, -4) and R (-2, -5) lie on the graph indicating that x =, y = -4 and x = -2, y = -5 are some other solutions of the equation.


 





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