Question

Which of the following linear equations would
be parallel to each other when plotted on a graph?
A: 5x + 7y + 10 = 0
B: x + y + 10 = 0
C: x + 5y + 10 = 0
A and B
a.
A and C
b.
B and C
C.
d. All of them​

Answer 1

Answer:

option a.A and B

Step-by-step explanation:

because they are coincident

Answer 2

Answer:

All the three equations are not parallel to each other while plotting .

Step-by-step explanation:

Given :- Given equation are ,

$5x+7y+10 = 0 \\x+y+10 = 0 \\x+5y+10 = 0$

To find :- which two equations , will be parallel when plotted on graph .

Solution :-

Step 1) Condition for parallel lines is :- $\frac{a_1}{a_2} =\frac{b_1}{b_2} \neq \frac{c_1}{c_2}$  ---- ( a )  

Given equation are ,

$5x+7y+10 =0 \\x+y+10 = 0 \\x+5y+10 = 0$   ------ (1), (2) , (3) .

Step 2) We will solve sets of 2 equation simultaneously .

(A) eqn. (1) and (2)

$5x+7y+10 =0 \\x+y+10 = 0$  

$a_1 = 5 , a_2 = 1 ; b_1 = 7 , b_2 = 1 ; c_1 = 10 , c_2 = 10$

$\frac{a_1}{a_2} = \frac{5}{1}$ --- (4)

$\frac{b_1}{b_2} =\frac{7}{1}$ ----- (5)

$\frac{c_1}{c_2} =\frac{10 }{10}$ ---- (6)

from eqn. (4) , (5) , (6)

we get that ,

$\frac{a_1}{a_2} \neq \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

then these linear equations (A) and (B)  are not parallel .

Step 3)

(B) eqn. (2) and (3)

$x+y+10 = 0 \\x+5y+10 = 0$  

comparing equations , we get

$a_1 = 1 , a_2 = 1 ; b_1 = 1 , b_2 = 5 , c_1 =10 , c_2 = 10$

$\frac{a_1}{a_2} =\frac{1}{1}$ ---- (7)

$\frac{b_1}{b_2} =\frac{1}{5}$ ---- (8)  

$\frac{c_1}{c_2} =\frac{10}{10}$ --- (9)

from eqn. (7) , (8) , (9)

we get that $\frac{a_!}{a_2} \neq \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

Hence , they are not parallel .

Step 3)

(C) eqn. (1) and (3)

$5x +7y+10 = 0 \\x+5y+10 = 0$

comparing equations ,

we get,

$a_1 = 5 , a_2 = 1 ; b_1 = 7 , b_2 = 5 ; c_1 = 10 , c_2 = 10$

$\frac{a_1}{a_2} =\frac{5}{1}$ --- (10)

$\frac{b_1}{b_2} =\frac{7}{5}$  ---- (11)

$\frac{c_1}{c_2} =\frac{10}{10 }$  ----- (12)

from eqn. (10) , (11) , (12)

we get that ,

linear equations are not parallel .

Thus , answer :- all the three equations are not parallel to each other while plotting .

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