Graphically, the pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(A) intersecting at exactly one point. (B) intersecting at exactly two points.
(C) coincident (D) parallel
NCERT Class X
Mathematics - Exemplar Problems
Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Answers
Compare the equations with:
6x-3y+10=0
2x-y+9=0
We get
a1 = 6
a2=2
b1=-3
b2=-1
c1=10
c2=9
a1/a2=6/2
=3
b1/b2=-3/-1
=3
c1/c2
=10/9
a1/a2=b1/b2≠c1/c2
So the equation has no solution
Hence the lines are parallel.
Option D is correct.
Hope it helps.
Given :
The pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
To check :
if lines are :
(A) intersecting at exactly one point. (B) intersecting at exactly two points.
(C) coincident (D) parallel
Step-by-step explanation:
The given equations are,
6x-3y+10 = 0
On dividing by 3, we get
⇒ 2x-y+ 10/3= 0… (i)
And 2x-y+9=0…(ii)
The table for 2x-y+ 10/3 = 0, is given below
x 0 -5/3
y 10/3 0
The table for 2x-y+9=0, is given below
x 0 -9/2
y 9 0
The correct answer is option (D) Parallel
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