Question

The number of solutions of the pair of linear equations $\tfrac{4}{3}x + 2y = 8$, $2x + 3y = 12$ will be:
 

• A. Only one
• B. Infinite
• C. Two
• D. None

Hint:

For linear equations $a_1x+b_1y=c_1$ and $a_2x+b_2y=c_2$: - If $\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$, unique solution. - If $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$, infinite solutions. - If $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$, no solution.

Answer 1

The Correct Option is A

Step 1: Write equations in standard form
Equation 1: $\dfrac{4}{3}x + 2y = 8 $\Rightarrow$ 4x + 6y = 24$
Equation 2: $2x + 3y = 12$

Step 2: Compare coefficients
Equation 1: $4x + 6y = 24$
Equation 2: $2x + 3y = 12$
Divide Equation 1 by 2: $2x + 3y = 12$
This is exactly Equation 2.

Step 3: Interpret result
Both equations are identical, meaning they represent the same line.
Thus, there are infinitely many solutions.

Step 4: Correction
So the correct answer is (B) Infinite.