Question

14. Check whether the given pair of linear equations are consistent or
not
2x + 2 y = 5
3x + 4y = 6​

Answer 1

Step-by-step explanation:

Given:-

The pair of linear equations are :

2x + 2 y = 5

3x + 4y = 6

To find:-

Check whether the given pair of linear equations are consistent or not 2x + 2 y = 5 and 3x + 4y = 6

Solution:-

Given pair of linear equations in two variables are

2x + 2 y = 5

=> 2x+2y-5 = 0

On Comparing this with a1x+b1y+c1=0

a1 = 2 , b1 = 2 , c1=-5

and

3x + 4y = 6

=> 3x+4y -6=0

On Comparing this with a2x+b2y+c2=0

a2=3,b2 = 4 , c2 = -6

a1/a2 = 2/3

b1/b2=2/4 = 1/2

c1/c2 = -5/-6=5/6

we have

a1/a2 ≠ b1/b2 ≠ c1/c2

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

Answer:-

The given pair of linear equations in two variables are Consistent lines.

Used formulae:-

• If a1/a2 ≠ b1/b2 ≠ c1/c2 then a1x+b1y+c1=0 and a2x+b2y+c2=0 are consistent and dependent lines or intersecting lines.

• They have a unique (only one) solution.