Question

Find b for which the following systems of equations have unique 9x + by -1 =0 & 3x+4y-2 =0​

Answer 1

Answer:

ɢɪᴠᴇɴ, ᴘᴀɪʀ ᴏғ ᴇǫᴜᴀᴛɪᴏɴs

9x+ᴘʏ−1=0 ᴀɴᴅ 3x+4ʏ−2=0

ᴏɴ ᴄᴏᴍᴘᴀʀɪɴɢ ᴛʜᴇ ɢɪᴠᴇɴ ᴇǫᴜᴀᴛɪᴏɴ ᴡɪᴛʜ sᴛᴀɴᴅᴀʀᴅ ғᴏʀᴍ

ɪ.ᴇ. ᴀ1x+ʙ1ʏ+ᴄ1=0 ᴀɴᴅ ᴀ2x+ʙ2ʏ+ᴄ2=0, 

ᴡᴇ ɢᴇᴛ ᴀ1=9,ʙ1=ᴘ ᴀɴᴅ ᴄ1=−1

ᴀɴᴅ ᴀ2=3,ʙ2=4 ᴀɴᴅ ᴄ2=−2

ғᴏʀ ᴜɴɪǫᴜᴇ sᴏʟᴜᴛɪᴏɴs,

ᴀ2ᴀ1=ʙ2ʙ1 

ᴀ2ᴀ1=39,  ʙ2ʙ1=4ᴘ

ʜᴇʀᴇ,

∴3=4ᴘ

ᴏɴ ᴛᴀᴋɪɴɢ ɪ ᴀɴᴅ ɪɪ ᴛᴇʀᴍs, ᴡᴇ ɢᴇᴛ 

ᴘ=12

ᴛʜᴜs, ɢɪᴠᴇɴ ʟɪɴᴇs ʜᴀᴠᴇ ᴀ ᴜɴɪǫᴜᴇ sᴏʟᴜᴛɪᴏɴ ғᴏʀ ᴀʟʟ ʀᴇᴀʟ ᴠᴀʟᴜᴇs ᴏғ ᴘ, ᴇxᴄᴇᴘᴛ 12.

Step-by-step explanation:

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