1.

The point of intersection of the lines 2x - 5y = 6 and x + y = 3 is:a) (0,3) by (3,0)c) (3,3)d) (0,0)​

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Answer:Hi hope this helps:)

Step-by-step explanation:

Line passing through point of intersecting of L  

1

​  

,L  

2

​  

 is given by L  

1

​  

+λ  

2

​  

=0

⇒(3x+2y+4)+λ(2x+5y−1)=0

⇒X(3+2λ)+y(2+5λ)+4−λ=0

Distance of (2,−1) to this line,

∣

∣

∣

∣

∣

∣

​  

 

(3+2λ)  

2

+(2+5λ)  

2

 

​  

 

2(3+2λ)−(2+5λ)+4−λ

​  

 

∣

∣

∣

∣

∣

∣

​  

=2

⇒6+4λ−2−5λ=2  

29λ  

2

+32λ+13

​  

 

⇒−2λ+8=2  

29λ  

2

+32λ+13

​  

 

⇒λ  

2

+16−8d=29λ  

2

+32λ+13

⇒28λ  

2

+40λ−3=0⇒28λ  

2

+42λ−2λ−3=0

                                           14λ(2λ+3)−(2λ+3)=0

(14λ−1)(2λ+3)=0⇒λ=  

14

1

​  

 or λ=  

2

−3

​  

 

L:x(3+  

7

1

​  

)+y(2+  

14

5

​  

)+4−  

14

1

​  

=0

44x+33y+55=0⇒  

4x+3y+5=0

​  

 

or  x(3−3)+y(2−  

2

15

​  

)+4+  

2

3

​  

=0

⇒y(−11)+11=0⇒  

y=1

​ srry if its in bad ORDER


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