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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