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| An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear. |
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A linear equation in two variables is of the form ax + by = c, where  |
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| Example: |
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| 2x + 3y = 5, x - 2y = 6, -6x + y =8 |
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| A pair of values of x and y that satisfy a given linear equation in two variables is said to be its solution. |
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| Example: |
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| x = 1, y = 1 is a solution of 2x + 3y = 5 |
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| 2(1) + 3(1) = 5 |
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| x = -2, y = 3 is also a solution of 2x + 3y = 5 |
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| 2(-2) + 3(3) = 5 |
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| -4 + 9 = 5 |
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| Similarly, we can find many more solutions for 2x + 3y = 5 |
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| A linear equation in two variables has infinitely many solutions. |
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| Example 1: |
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| Find four solutions of the equation 2x + y = 5. |
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| Suggested answer: |
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| 2x + y = 5 |
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| y = 5 - 2x |
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| Put x = 0, y = 5 |
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| x = 1, y = 5 - 2 = 3 |
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| x = 2, y = 5 - 4 = 1 |
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| x = 3, y = 5 - 6 = -1 |
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Linear equations in two variables
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