Solve for x and y: 4x - 3y = 8, 6x - y = \(\frac{29}3\)

1.	Solve for x and y: 4x - 3y = 8, 6x - y = \(\frac{29}3\)
Answer» The given system of equation is: 4x - 3y = 8 ……(i) 6x - y = \(\frac{29}3\)........(ii) On multiplying (ii) by 3, we get: 18x – 3y = 29 ….(iii) On subtracting (iii) from (i) we get: -14x = -21 x = \(\frac{21}{14}=\frac{3}2\) Now, substituting the value of x = \(\frac{3}2\) in (i), we get: 4 x \(\frac{3}2\)- 3y = 8 ⇒ 6 – 3y = 8 ⇒ 3y = 6 – 8 = -2 y = \(\frac{-2}3\) Hence, the solution x = \(\frac{3}2\) and y = \(\frac{-2}3\).

Answer»

The given system of equation is:

4x - 3y = 8 ……(i)

6x - y = \(\frac{29}3\)........(ii)

On multiplying (ii) by 3, we get:

18x – 3y = 29 ….(iii)

On subtracting (iii) from (i) we get:

-14x = -21

x = \(\frac{21}{14}=\frac{3}2\)

Now, substituting the value of x = \(\frac{3}2\) in (i), we get:

4 x \(\frac{3}2\)- 3y = 8

⇒ 6 – 3y = 8

⇒ 3y = 6 – 8 = -2

y = \(\frac{-2}3\)

Hence, the solution x = \(\frac{3}2\) and y = \(\frac{-2}3\).

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