MHT CET · Maths · Pair of Lines
The number of integer values of \(m\), for which \(x\)-coordinate of the point of intersection of the lines \(3 x+4 y=9\) and \(y=m x+1\) is also an integer, is
- A 2
- B 0
- C 4
- D 1
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
By solving \(3 x+4 y=9, y=m x+1\), we get
\(x=\frac{5}{3+4 \mathrm{~m}}\)
Now, \(x\) is an integer, if \(3+4 \mathrm{~m}=1,-1,5,-5\)
\(\therefore \quad \mathrm{m}=\frac{-2}{4}, \frac{-4}{4}, \frac{2}{4}, \frac{-8}{4}\).
Since, \(\mathrm{m}=\frac{-2}{4}, \frac{2}{4}\) do not give integral values of \(m\).
\(\therefore \quad \mathrm{m}\) has two integer values.
\(x=\frac{5}{3+4 \mathrm{~m}}\)
Now, \(x\) is an integer, if \(3+4 \mathrm{~m}=1,-1,5,-5\)
\(\therefore \quad \mathrm{m}=\frac{-2}{4}, \frac{-4}{4}, \frac{2}{4}, \frac{-8}{4}\).
Since, \(\mathrm{m}=\frac{-2}{4}, \frac{2}{4}\) do not give integral values of \(m\).
\(\therefore \quad \mathrm{m}\) has two integer values.
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