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Question for you(reupload):-

Find the interval of mm of each case, where there are 0, 1, 2, 3, or 4 solutions to the following system equation. (x and y are real-valued.)


$\begin{cases} & |x-1|+|y+1|=1\\&x^{2}+y^{2}=m^{2}\end{cases}$

$\large\text{\underline{Note:-{}}}$
Apply coordinate geometry.​​​

Answer 1

Answer:

Consider the system of linear equations

x+ky+3z=0 ..(1)

3x+ky−2z=0 ..(2)

2x+4y−3z=0 ..(3)

Solving the above determinant equation, we get

−3k+8−k(−9+4)+3(12−2k)=0

⇒k=11

Solving equations (1), (2) and (3), we get

2x=5z & 3x=−(k+4)y

⇒2x=5z&x=−5y