9th Maths 4.2
NCERT Class 9th solution of Exercise 4.1
NCERT Class 9th solution of Exercise 4.3
NCERT Class 9th solution of Exercise 4.4
Exercise 4.2
Q1. Which one of the following options is true, and why?
`y=3x+5`has
i) a unique solution, ii) only two solutions, iii) infinitely many solutions.
Answer :
iii) because a linear equation in two variables has infinitely many solutions.
Q2. Write four solutions for each of the following equations :
i) `2x+y=7` ii) `πx+y=9` iii) `x=4y.`
Sol. :
i) `2x+y=7`
then `y=7-2x`
when `x=0`
`y=7-2(0)`
`y=7-0`
`y=7`
when `x=1`
`y=7-2(1)`
`y=7-2`
`y=5`
when `x=2`
`y=7-2(2)`
`y=7-4`
`y=3`
when `x=3`
`y=7-2(3)`
`y=7-6`
`y=1`
Answer :
Required four solutions are `(0, 7), (1, 5), (2, 3),` and `(3, 1)`.
ii) `πx+y=9`
then
`y=9-πx`
when `x=0`
`y=9-0`
`y=9`
when `x=1`
`y=9-π1`
`y=9-π`
when `x=-1`
`y=9-π(-1)`
`y=9+π`
When `x=frac(9)(π)`
`y=9-πfrac(9)(π)`
`y=9-9`
`y=0`
Answer :
Required four solutions are `(0, 9), (1, 9-π), (-1, 9+π)`, and `(frac(9)(π), 0)`.
iii) `x=4y`
when `y=0`
`x=4(0)`
`x=0`
when `y=1`
`x=4(1)`
`x=4`
when `y=-1`
`x=4(-1)`
`x=-4`
when `y=frac(1)(2)`
`x=4(frac(1)(2))`
`x=2`
Answer :
Required four solutions are `(0, 0), (4, 1), (-4, -1)`, and `(2, frac(1)(2))`
Q3. Check which of the following are the solutions of the equation `x-2y=4` and which are not :
i) `(0, 2)` ii) `(2, 0)` iii) `(4, 0)` iv) `(sqrt2, 4sqrt2)` v) `(1, 1)`
Sol. :
Given equation is `x-2y=4`
then `x-2y-4=0`
i) Put `(0, 2)`
`0-2(2)-4=0`
`0-4-4=0`
`-8≠0`
ii) Put `(2, 0)`
`2-2(0)-4=0`
`2-4=0`
`-2≠0`
iii) Put `(4, 0)`
`4-2(0)-4=0`
`4-4=0`
`0=0`
iv) Put `(sqrt2, 4sqrt2)`
`sqrt2-2(4sqrt2)-4=0`
`sqrt2-8sqrt2-4=0`
`-7sqrt2-4≠0`
v) Put `(1, 1)`
`1-2(1)-4=0`
`1-2-4=0`
`-5≠0`
Answer :
`(4, 0)` is a solution but `(0, 2), (2, 0), (sqrt2, 4sqrt2)` and `(1, 1)` are not solution of the equation.
Q4. Find the value of `k`, if `x=2, y=1` is a solution of the equation `2x+3y=k.`
Sol. :
Given equation `2x+3y=k`
we put the `x=2` and `y=1`
`2(2)+3(1)=k`
`4+3=k`
`7=k`
Answer :
The required value of `k=7`.
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