Question

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→ Find the point of intersection if : x + y = 6 and x - y = 4

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Answer 1

Question ;

Find the intersection of two lines :

x+ y = 6 and x - y = 4

Theory :

Point of intersection means the point at which two lines intersect.

• Let the equations of two intersecting straight lines be:

$\sf \: a_{1}x + b_{1}y + c_{1} = 0 \: \: ...(1)$

$\sf \: a_{2}x + b_{2}y + c_{2} = 0...(2)$

Suppose the above equations of two intersecting lines intersect at P (h,k)

• Then (h,k) satisfy both the equations (1) and (2) .

Now solve the two equations .

Solution :

We have to find the intersection of two lines :

$\sf \: x + y = 6..(1)$

$\sf \: x - y = 4...(2)$

For finding point of intersection,Solve the equations (1) and (2)

Add (1) and (2)

$\implies \sf \: x + y + x - y = 4 + 6$

$\sf \implies \: 2x = 10$

$\sf \implies \: x = \frac{10}{2} = 5$

Now put x = 5 in equation (1)

$\sf \implies5 + y = 6$

$\sf \implies \: y = 6 - 5 = 1$

Therefore ,point of intersection of two lines is (5,1)

Note :

• Graphs of x+y = 6
• and x-y = 4
• in the attachment

Answer 2

ᴛʜᴇ ɢɪᴠᴇɴ ᴇϙᴜᴀᴛɪᴏɴs ᴀʀᴇ-

x + ʏ = 6         --------------- 1

x - ʏ = 4          --------------- 2

ᴀᴅᴅɪɴɢ ʙᴏᴛʜ ᴇϙᴜᴀᴛɪᴏɴs  

(x + ʏ) + (x - ʏ) = 6 + 4

x + ʏ + x -ʏ = 10

2x = 10

x = 5

ᴘᴜᴛ x = 5 ɪɴ ᴇϙᴜᴀᴛɪᴏɴ 2

x - ʏ = 4

5 - ʏ = 4

-ʏ = 4 - 5

-ʏ = -1

ʏ = 1

ʜᴇɴᴄᴇ, ʙᴏᴛʜ ʟɪɴᴇs ᴀʀᴇ ɪɴᴛᴇʀsᴇᴄᴛɪɴɢ ᴀᴛ ᴘᴏɪɴᴛ (5, 1).