Solve for x and y: x – y = 3, \(\frac{x}3+\frac{y}2=6\)

1.	Solve for x and y: x – y = 3, \(\frac{x}3+\frac{y}2=6\)
Answer» The given system of equations is x – y = 3 …..(i) \(\frac{x}3+\frac{y}2= 6 \)........(ii) From (i), write y in terms of x to get y = x – 3 Substituting y = x – 3 in (ii), we get \(\frac{x}3+\frac{x-3}2= 6 \) ⇒ 2x + 3(x – 3) = 36 ⇒ 2x + 3x – 9 = 36 ⇒ x = \(\frac{45}5= 9\) Now, substituting x = 9 in (i), we have 9 – y = 3 ⇒ y = 9 – 3 = 6 Hence, x = 9 and y = 6.

Answer»

The given system of equations is

x – y = 3 …..(i)

\(\frac{x}3+\frac{y}2= 6 \)........(ii)

From (i), write y in terms of x to get

y = x – 3

Substituting y = x – 3 in (ii), we get

\(\frac{x}3+\frac{x-3}2= 6 \)

⇒ 2x + 3(x – 3) = 36

⇒ 2x + 3x – 9 = 36

⇒ x = \(\frac{45}5= 9\)

Now, substituting x = 9 in (i), we have

9 – y = 3

⇒ y = 9 – 3 = 6

Hence, x = 9 and y = 6.

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