Write four solutions for each of the following equations: (i) 2x + y = 7 (ii) πx + y = 9 (iii) x = 4y

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

For x = 0,
2(0) + y = 7
⇒ y = 7
Therefore, (0, 7) is a solution of this equation.
For x = 1,
2(1) + y = 7
⇒ y = 5
Therefore, (1, 5) is a solution of this equation.
For x = −1,
2(−1) + y = 7
⇒ y = 9
Therefore, (−1, 9) is a solution of this equation.
For x = 2,
2(2) + y = 7
⇒y = 3

Therefore, (2, 3) is a solution of this equation.

(ii) πx + y = 9

For x = 0,
π(0) + y = 9
⇒ y = 9
Therefore, (0, 9) is a solution of this equation.
For x = 1,
π(1) + y = 9
⇒y = 9 − π
Therefore, (1, 9 − π) is a solution of this equation.
For x = 2,
π(2) + y = 9
⇒ y = 9 − 2π
Therefore, (2, 9 −2π) is a solution of this equation.
For x = −1,
π(−1) + y = 9
⇒ y = 9 + π
⇒ (−1, 9 + π) is a solution of this equation.

(iii) x = 4y

For x = 0,
0 = 4y
⇒ y = 0
Therefore, (0, 0) is a solution of this equation.
For y = 1,
x = 4(1) = 4
Therefore, (4, 1) is a solution of this equation.
For y = −1,
x = 4(−1)
⇒ x = −4
Therefore, (−4, −1) is a solution of this equation.