Question

one equation of a pair of dependent linear equations is -5x+7y=2 the second equation can be:
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Answer 1

Answer:

solution :-

x=1 , then y =1

x=0 , then y =2/7

Step-by-step explanation:

Answer 2

$\bf\huge\underline{Question}$⠀⠀

One equation of a pair of dependent linear equations is -5x+7y=2. The second equation can be

$\bf\huge\underline{Solution}$

Given equation of line is

-5x + 7y - 2 = 0

Compare with ${a_1x}$ + ${b_1y}$ + ${c_1}$ = 0, we get

⠀⠀${a_1}$ = -5, ${b_1}$ = 7, ${c_1}$ = -2

Since condition for dependent linear equation is

⠀⠀$\dfrac{a_1}{a_2}$ = $\dfrac{b_1}{b_2}$ = $\dfrac{c_1}{c_2}$ = $\dfrac{1}{k}$

∴ $\dfrac{-5}{a_2}$ = $\dfrac{7}{b_2}$ = $\dfrac{2}{c_2}$ = $\dfrac{2}{k}$

=> ${a_2}$ = -5k, ${b_2}$ = 7k, ${c_2}$ = -2k

where, k is any arbitrary constant

Substituting k = 2, then

⠀⠀${a_2}$ = -10, ${b_2}$ = 14 and ${c_2}$ = -4

∴ The required equation of line becomes

⠀⠀-10x + 14y - 4 = 0

=> 10x - 14y + 4 = 0 => 10x - 14y = -4