1.

If x = 2 – α and y = 2 + α is a solution of the equation 3x – 2y + 6 = 0, find the value of ‘α’. Find three more solutions of the resultant equation.

Answer»

Given that x = 2 – α and y = 2 + α is a solution of 3x – 2y + 6 = 0 

Thus 3 (2 – α) – 2 (2 + α) + 6 = 0 

⇒ 6 – 3α – 4 – 2α + 6 = 0 

⇒ -5α + 8 = 0

 ⇒ -5α = -8 

∴ α = 8/5

Three more solutions are

x03x – 2y = -6
3x – 2(0) = -6
y = -6/3 = -2		1
y3x – 2y = -6
3(0) – 2y = -6		03x – 2y = -6
3(1) – 2y = -6
y = 9/2
Solutions(0, 3)(-2, 0)(1, 9/2)


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