Maths-
General
Easy
Question
Determine whether the following equations have unique solution y = 2x + 5
y = 3x – 2.
Hint:
An Equation is said to have Unique solution when there exists only one point, on substituting which, LHS = RHS.
For Equations with Unique solution (One solution):-
(a1/a2) ≠ (b1/b2)
Where a1, a2 are the coefficients of variable x in both the equations i & ii, respectively
and b1, b2 are the coefficients of variable y in both the equations i & ii, respectively.
The correct answer is: The given equations y = 2x + 5 and y = 3x – 2 have unique solution
Step-by-step solution:-
y = 2x + 5
∴ -2x + y = 5 ….............................................. (Taking variables and constants on either sides of the equation)
i.e. 2x - y = -5 …......................... (Multiplying both sides by -1) ....................................................................................... (Equation i)
y = 3x – 2
∴ -3x + y = -2 ….............................................. (Taking variables and constants on either sides of the equation)
i.e. 3x - y = 2 …......................... (Multiplying both sides by -1) ....................................................................................... (Equation ii)
Comparing Equations i & ii with the standard form of a linear equation in 2 variables, i.e. ax + by = c, we get-
a1 = 2; b1 = -1; c1 = -5 and
a2 = 3; b2 = -1; c2 = 2
Now, we calculate a1/a2 and b1/b2 and check whether the 2 are equal or not.
a1/a2 = 2/3 = 0.67 ............................................................................................................................................................ (Equation iii)
b1/b2 = -1/-1 = 1 .............................................................................................................................................................. (Equation iv)
From Equations iii & iv, We observe that-
a1/a2 ≠ b1/b2 for the given Equations.
∴ The given Equations have Unique solution.
Final Answer:-
∴ The given equations y = 2x + 5 and y = 3x – 2 have unique solution.
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