Question

Write four solutions for each of the following equations:

(i) 2x + y = 7 (ii) πx + y = 9 (iii) x = 4y

Answer 1

(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.

For x = 2,

2 = 4y

⇒

Therefore, is a solution of this equation.