Chapter 4 Linear Equations in Two Variables Exercise 4.2
Question 1: 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) infinitely many solutions is the correct option as a linear equation in two variables has many solutions i.e. infinite solutions.
Question 2: Write four solutions for each of the following equations:
(i) 2x + y = 7 (ii) πx + y = 9 (iii) x = 4y
Answer:
i) 2x + y = 7
|
x |
2 |
1 |
3.5 |
0 |
|
y |
3 |
5 |
0 |
7 |
ii) πx + y = 9
|
x |
1 |
0 |
-1 |
9/π |
|
y |
π - 9 |
9 |
9 + π |
0 |
iii) x = 4y
|
x |
0 |
4 |
-4 |
2 |
|
y |
0 |
1 |
-1 |
1/2 |
Question 3: Check which of the following are solutions of the equation x - 2y = 4 and which are not:
(i) (0, 2) (ii) (2, 0) (iii) (4, 0) (iv) (√2 , 4√2) (v) (1, 1)
Answer:
For i) (0, 2)
x - 2y = 4
= (0) - 2(2) = 4
= 0 - 4 = 4
= -4 ≠ 4
For ii) (2, 0)
x - 2y = 4
= (2) - 2(0) = 4
= 2 - 0 = 4
= 2 ≠ 4
For iii) (4, 0)
x - 2y = 4
= (4) - 2(0) = 4
= 4 - 0 = 4
= 4 = 4
For iv) (√2 , 4√2)
x - 2y = 4
= (√2) - 2(4√2) = 4
= √2 - 8√2 = 4
= -7√2 ≠ 4
For v) (1, 1)
x - 2y = 4
= (1) - 2(1) = 4
= 1 - 2 = 4
= -1 ≠ 4
Therefore option iii) is solution for x - 2y = 4.
Question 4: Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Answer:
If x = 2 and y = 1, then the value of k in 2x + 3y = k is
2(2) + 3(1) = k
= 4 + 3 = k
= 7 = k
Hence k = 7.
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