Find the value of a, if point (2,2) is present on the graph of equation 4x + ay = 14
Answers
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be Rs. x and that of a pen to be Rs. y).
Sol: Let the cost of a notebook = Rs x
The cost of a pen = y
According to the condition, we have
[Cost of a notebook] = 2 × [Cost of a pen]
i.e. [x] = 2 × [Y]
or x = 2y
or x – 2y = 0
Thus, the required linear equation is × – 2y = 0.
2. Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) (ii) (iii) –2x + 3y = 6 (iv) x = 3y
(v) 2x = –5y (vi) 3x + 2 = 0 (vii) y – 2 = 0 (viii) 5 = 2x
Sol: (i) We have
Comparing it with ax + bx + c = 0, we have a = 2, b = 3 and
(ii) We have
Comparing with ax + bx + c = 0, we get
Note: Above equation can also be compared by:
Multiplying throughout by 5,
or 5x – y – 50 = 0
or 5(x) + (–1)y + (–50) = 0
Comparing with ax + by + c = 0, we get a = 5, b = –1 and c = –50.
(iii) We have –2x + 3y = 6
⇒ –2x + 3y – 6 = 0
⇒ (–2)x + (3)y + (–6) = 0
Comparing with ax + bx + c = 0, we get a = –2, b = 3 and c = –6.
(iv) We have x = 3y
x – 3y = 0
(1)x + (–3)y + 0 = 0
Comparing with ax + bx + c = 0, we get a = 1, b = –3 and c = 0.
(v) We have 2x = –5y
⇒ 2x + 5y =0
⇒ (2)x + (5)y + 0 = 0
Comparing with ax + by + c = 0, we get a = 2, b = 5 and c = 0.
(vi) We have 3x + 2 = 0
⇒ 3x + 2 + 0y = 0
⇒ (3)x + (10)y + (2) = 0
Comparing with ax + by + c = 0, we get a = 3, b = 0 and c = 2.
(vii) We have y – 2 = 0
⇒ (0)x + (1)y + (–2) = 0
Comparing with ax + by + c = 0, we have a = 0, b = 1 and c = –2.
(viii) We have 5 = 2x
⇒ 5 – 2x = 0
⇒ –2x + 0y + 5 = 0
⇒ (–2)x + (0)y + (5) = 0
Comparing with ax + by + c = 0, we get a = –2, b = 0 and c = 5.
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