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Finding Solution for Consistent Pair of Linear Equations

On solving 2 ...

Question

On solving $2 x + 3 y = 18, x - 2 y = 2,$ we get:
(a) x = 3, y = 4
(b) x = 6, y = 2
(c) x = 0, y = 6
(d) x = 3, y = 4

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Solution

The correct option is (b).

2x + 3y = 18 ....(i)
x − 2y = 2 ....(ii)
On multiplying (ii) by 2, we get:
2x − 4y = 4 ....(iii)
On subtracting (iii) from (i), we get:
7y = 14 ⇒ y = 2
On substituting y = 2 in (i), we get:
2x + 6 = 18 ⇒ 2x = 12 ⇒ x = 6
∴ x = 6 and y = 2

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(i) 2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
(ii) 2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
(iii) x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
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\frac{2}{3} x + 5 y = 12, x + \frac{3}{2} y = 6,

we get:
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(b) x = 6, y = 1
(c) x = −3, y = −2
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