Question

Show that the lines x-y-1=0 , 4x+3y=25 and 2x-3y+1=0 are concurrent​

Answer 1

Answer:

25

Step-by-step explanation:

Given, x−y−1=0 , 4x+3y=k & 2x−3y+1=0  

The given lines are concurrent i.e. all of them intersect at same  point

Taking the above 2 equations:

x−y−1=0   -----------(i)              

2x−3y+1=0  ----------(ii)

Multiplying 3 both side of eq. (i)

3[x−y−1]=0

3x−3y−3=0 -------------(iii)

Now, equating (ii) & (iii)

3x

2x

​  

 

−3y

−3y

​  

 

−3=0

+1=0

​  

 

−+−

x−4=0

​  

 

⇒x=4

∴2(4)−3y+1=0

⇒8−3y+1=0

⇒3y=9

⇒y=3

∴ Point of intersection of 3  lines is (4,3)

This pt. lies on the line 4x+3y=k

⇒4(4)+3(3)=k      

k=25