Show that (3, 1) as well as (2, −2) are the solutions of the equation 3x − y = 8. Find two more solutions. How many solutions can we find?

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Solution

Given equation: $3 x - y = 8$

To show: $(3, 1), (2, - 2)$ are the solutions of the given equation.

Putting $x = 3, y = 1$ in the equation, we get:
$L H S = 3 \times 3 - 1 = 9 - 1 = 8 = R H S$
Now, putting $x = 2, y = - 2$ in the equation, we get:
$L H S = 3 \times 2 - (- 2) = 6 + 2 = 8 = R H S$
Hence $(3, 1), (2, - 2)$ are the solutions of $3 x - y = 8$ .

Further solutions:
The equation can be rewritten as $y = 3 x - 8$

Putting $x = 1$ , we get: $y = 3 - 8 = - 5$
Putting $x = 4$ , we get: $y = 3 \times 4 - 8 = 4$
Putting $x = 5$ , we get: $y = 3 \times 5 - 8 = 7$ .....and so on
Two more solutions are $(1, - 5) and (4, 4) .$
Hence, we can find infinite solutions for the given equation.

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