Solve for x and y: 2x – y + 3 = 0, 3x – 7y + 10 = 0

1.	Solve for x and y: 2x – y + 3 = 0, 3x – 7y + 10 = 0
Answer» The given system of equation is: 2x – y + 3 = 0…….(i) 3x – 7y + 10 = 0 ……(ii) From (i), write y in terms of x to get y = 2x + 3 Substituting y = 2x + 3 in (ii), we get 3x – 7(2x + 3) + 10 = 0 ⇒ 3x – 14x – 21 + 10 = 0 ⇒ -7x = 21 – 10 = 11 x = - \(\frac{11}7\) Now substituting x = – \(\frac{11}7\) 7 in (i), we have - \(\frac{22}7\) - y + 3 = 0 y = 3 - \(\frac{22}7\) = - \(\frac{1}7\) Hence, x = – \(\frac{11}7\) and y = - \(\frac{1}7\).

Answer»

The given system of equation is:

2x – y + 3 = 0…….(i)

3x – 7y + 10 = 0 ……(ii)

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

y = 2x + 3

Substituting y = 2x + 3 in (ii), we get

3x – 7(2x + 3) + 10 = 0

⇒ 3x – 14x – 21 + 10 = 0

⇒ -7x = 21 – 10 = 11

x = - \(\frac{11}7\)

Now substituting x = – \(\frac{11}7\) 7 in (i), we have

- \(\frac{22}7\) - y + 3 = 0

y = 3 - \(\frac{22}7\) = - \(\frac{1}7\)

Hence, x = – \(\frac{11}7\) and y = - \(\frac{1}7\).

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