Question

Find the solution of the form x=a ,y=0 and x=o ,y=b for the following equation 2x+5y=10 and 2x+3y=6

Answer 1

First,
2 x a +3 x 0 = 10
a = 5
Now,
2 x 0 + 3 x b = 6
b = 2

Answer 2

AnswEr:

Substituting x = 0 in the equation 2x + 5y = 10, we get

$\Rightarrow$ $\sf\quad{2\times\:0+5y=10}$

$\Rightarrow$ $\sf\quad{5y=10}$

$\Rightarrow$ $\sf\quad{y=2}$

Thus, x = 0 and y = 2 is a solution of 2x + 5y = 10.

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Substituting y = 0 in 2x + 5y = 10, we get

$\sf\quad{2x+5\times\:0=10\implies\:2x=10\implies\:x=5}$

Thus, x = 5 and y = 0 is a solution of 2x + 5y = 10.

Thus, x = 5, y = 0 and x = 0, y = 2 are two solutions of 2x + 5y = 10.

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Now, $\sf{Consider\:the\:equation\:2x+3y=6}$

Substituting x = 0, in this equation, we get

$\sf\quad{2\times\:0+3y=6\implies\:3y=6\implies\:y=2}$

So, x = 0, y = 2 is a solution of 2x + 3y = 6.

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Substituting, y = 0 in 2x + 3y = 6, we get

$\sf\quad{2x+3\times\:0=6\implies\:2x=6\implies\:x=3}$

Thus, x = 0, y = 2 and x = 3, y = 0 are solutions of 2x + 3y = 6

Clearly, x = 0, y = 2 is common solution of the givem equations

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