Question

The number of solutions of the pair of equations 2x +5y =10 and 6x +15y −30 = 0 is

(a) 0 (b) 1 (c) 2 (d) infinite​

Answer 1

Answer:

2x+5y=10

6x+15y=30

that

6x+15y=30

- 6x+15y=30

0x+30y=30

30y=30

y=30

30

y=1

then 2x+5y=10

2x+5(1)=10

2x+5=10

2x=10-5

2x=5

X=5/2

Answer :- X=5/2 y= 1

Answer 2

Answer:

Option (d)

Step-by-step explanation:

Given:-

The pair of equations 2x +5y =10

and 6x +15y -30 = 0

To find:-

Find the number of solutions of the pair of equations ?

Solution:-

Given that:

The pair of linear equations in two variables

2x +5y =10

=> 2x + 5y -10 = 0

On comparing this with a1x+b1y+c1=0 then

a1 = 2

b1 = 5

c1 = -10

And

6x +15y -30 = 0

=> 3(2x+5y-10) = 0

=> 2x + 5y -10 = 0/3

=> 2x + 5y -10 = 0

On comparing this with a2x+b2y+c2=0 then

a2 = 2

b2 = 5

c2 = -10

a1/a2 = 2/2 = 1

b1/b2 = 5/5 = 1

c1/c2 = -10/-10 = 1

a1/a2 = b1/b2 = c1/c2

The pair of linear equations in two variables are consistent and dependent lines.

They have infinitely number of many solutions.

Answer:-

The number of solutions of the pair of linear equations is infinite.

Used formulae:-

a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are the pair of linear equations in two variables then

• a1/a2 = b1/b2 = c1/c2 then they are consistent and dependent lines with infinite number of many solutions.

Additional information:-

• a1/a2 ≠ b1/b2 ≠ c1/c2 then they are consistent and independent lines with a unique solution.

• a1/a2 = b1/b2 ≠c1/c2 then they are inconsistent and lines with no solution.