Question

# The system of equations 3x - 5y = 20 ; 6x - 10y = 40 has

- No solution
- Unique solution
- Infinitely many solutions
- Infinitely many solutions

Hint:

### 1. For Equations with Unique solution (One solution):-

(a1/a2) ≠ (b1/b2)

2. For Equations with Infinitely Many solutions:-

(a1/a2) = (b1/b2) = (c1/c2)

3. For Equations with No solutions:-

(a1/a2) = (b1/b2) ≠ (c1/c2)

## The correct answer is: Infinitely many solutions

### Step-by-step solution:-

3x - 5y = 20 ....................................................................................... (Equation i)

6x - 10y = 40 ..................................................................................... (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 = 3; b1 = -5; c1 = 20 and

a2 = 6; b2 = -10; c2 = 40

Now, we calculate a1/a2; b1/b2 and c1/c2 to check the corelation between the 3:-

a1/a2 = 3/6 = 1/2 ............................................................................................................................................................ (Equation iii)

b1/b2 = -5/-10 = 1/2 ....................................................................................................................................................... (Equation iv)

c1/c2 = 20/40 = 1/2 ......................................................................................................................................................... (Equation v)

From Equations iii, iv & v, We observe that-

a1/a2 = b1/b2 = c1/c2 for the given Equations.

∴ The given Equations have Infinitely Many Solutions.

Final Answer:-

∴ Option c i.e. Infinitely Many Solutions is the correct answer.

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The equation is defined as a mathematical statement with at least two terms containing variables or numbers that are equal.**Let's take an example:**

Assume the hours are "h" when attempting to equalize,

As per the given question, we can write the equation as:

12.73 + 0.06h = 13.48 - 0.14h

Rearrange the terms of h in the above equation,

0.06h + 0.14h = 13.48- 12.73

In the above equation, combine the corresponding terms,

0.2h = 0.75

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Thus, the stock prices will be the same in 3.75 hours.