on comparing the ratio a1/a2, b1/b2 and c1/c2 find out weather the lines representing the following pairs of linear equation intersect at a point. are parallel or coincident 6x-3y+10=02x-y+9=0 About the author Liliana
Answer:both lines are parallel Step-by-step explanation: (i) 5x – 4y + 8 = 0 7x + 6y – 9 = 0 Comparing these equation with a1x + b1y + c1 = 0 a2x + b2y + c2= 0 We get a1 = 5, b1 = -4, and c1 = 8 a2 =7, b2 = 6 and c2 = -9 a1/a2 = 5/7, b1/b2 = -4/6 and c1/c2 = 8/-9 Hence, a1/a2 ≠ b1/b2 Therefore, both are intersecting lines at one point. (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 Comparing these equations with a1x + b1y + c1 = 0 a2x + b2y + c2= 0 We get a1 = 9, b1 = 3, and c1 = 12 a2 = 18, b2 = 6 and c2 = 24 a1/a2 = 9/18 = 1/2 b1/b2 = 3/6 = 1/2 and c1/c2 = 12/24 = 1/2 Hence, a1/a2 = b1/b2 = c1/c2 Therefore, both lines are coincident (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 Comparing these equations with a1x + b1y + c1 = 0 a2x + b2y + c2= 0 We get a1 = 6, b1 = -3, and c1 = 10 a2 = 2, b2 = -1 and c2 = 9 a1/a2 = 6/2 = 3/1 b1/b2 = -3/-1 = 3/1 and c1/c2 = 12/24 = 1/2 Hence, a1/a2 = b1/b2 ≠ c1/c2 Therefore, both lines are parallel Reply
[tex]{\huge{\blue\longrightarrow{\texttt{\orange A\red N\green S\pink W\blue E\purple R\red}}}}[/tex][tex]{\bold\pink{》 ❥︎ \:ꀍꂦᖘꏂ \: ꓄ꀍꀤꌚ \: ꀍꏂ꒒ᖘꌚ \: ꌩꂦꀎ \:♡︎ 《}}[/tex] (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 Comparing these equations with a1x + b1y + c1 = 0 a2x + b2y + c2= 0 We get:- a1 = 6, b1 = -3, and c1 = 10 a2 = 2, b2 = -1 and c2 = 9 a1/a2 = 6/2 = 3/1 b1/b2 = -3/-1 = 3/1 and c1/c2 = 12/24 = 1/2 Hence, a1/a2 = b1/b2 ≠ c1/c2 Therefore, both lines are parallel Reply
Answer:both lines are parallel
Step-by-step explanation:
(i) 5x – 4y + 8 = 0
7x + 6y – 9 = 0
Comparing these equation with
a1x + b1y + c1 = 0
a2x + b2y + c2= 0
We get
a1 = 5, b1 = -4, and c1 = 8
a2 =7, b2 = 6 and c2 = -9
a1/a2 = 5/7,
b1/b2 = -4/6 and
c1/c2 = 8/-9
Hence, a1/a2 ≠ b1/b2
Therefore, both are intersecting lines at one point.
(ii) 9x + 3y + 12 = 0
18x + 6y + 24 = 0
Comparing these equations with
a1x + b1y + c1 = 0
a2x + b2y + c2= 0
We get
a1 = 9, b1 = 3, and c1 = 12
a2 = 18, b2 = 6 and c2 = 24
a1/a2 = 9/18 = 1/2
b1/b2 = 3/6 = 1/2 and
c1/c2 = 12/24 = 1/2
Hence, a1/a2 = b1/b2 = c1/c2
Therefore, both lines are coincident
(iii) 6x – 3y + 10 = 0
2x – y + 9 = 0
Comparing these equations with
a1x + b1y + c1 = 0
a2x + b2y + c2= 0
We get
a1 = 6, b1 = -3, and c1 = 10
a2 = 2, b2 = -1 and c2 = 9
a1/a2 = 6/2 = 3/1
b1/b2 = -3/-1 = 3/1 and
c1/c2 = 12/24 = 1/2
Hence, a1/a2 = b1/b2 ≠ c1/c2
Therefore, both lines are parallel
[tex]{\huge{\blue\longrightarrow{\texttt{\orange A\red N\green S\pink W\blue E\purple R\red}}}}[/tex][tex]{\bold\pink{》 ❥︎ \:ꀍꂦᖘꏂ \: ꓄ꀍꀤꌚ \: ꀍꏂ꒒ᖘꌚ \: ꌩꂦꀎ \:♡︎ 《}}[/tex]
(iii) 6x – 3y + 10 = 0
2x – y + 9 = 0
Comparing these equations with
a1x + b1y + c1 = 0
a2x + b2y + c2= 0
We get:-
a1 = 6, b1 = -3, and c1 = 10
a2 = 2, b2 = -1 and c2 = 9
a1/a2 = 6/2 = 3/1
b1/b2 = -3/-1 = 3/1 and
c1/c2 = 12/24 = 1/2
Hence, a1/a2 = b1/b2 ≠ c1/c2
Therefore, both lines are parallel