# Linear Equations in Two Variables - Class 9 : Notes

**(1) An equation of the form , where a, b, c are real numbers such that a and b not both zero is called a linear equation in two variables.
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**Â , where , which are not zero. So this is linear equation in two variables.**

*For Example:***(2) A linear equation in two variables has infinitely many solutions.
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**we have , there is many solution**

*For Example:Â*If we take , then

If we take , then

**(3) The graph of a linear equation in two variables is a straight line.
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*For Example:*

We have

When , we have:

When , we have:

When , we have:

Thus, we have the following table:Plotting the points (0, 4) (2, 2) and (4, 0) on the graph paper and drawing a line joining them.

**(4) The equations of x and y-axes are and respectively.
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*equation is for x-axes because in this equation .*

**For Example:**Â equation is for y-axes because in this equation .

**(5) The graph of the equation is a straight line parallel to y-axis.
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*The equation for such a line is given below:*

**For Example:****(6) The graph of the equation is a straight line parallel to x-axis.
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**For a line that is parallel to the x-axis, the equation for such a line is given below:**

*For Example:Â***(7) Every point on the graph of a linear equation in two variables is a solution of the equation. Conversely, every solution of linear equation in two variables represents a point on the graph of the equation.
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**In linear equation , also lies on this line.**

*For Example:Â*
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