CUET UG 2025 — General Test Quantitative Reasoning

Equation 1: $x + 4y - 3 = 0$x+4y−3=0

Equation 2: $2x + 8y - 6 = 0$2x+8y−6=0

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Multiplying Equation 1 by 2:

$$2 \times (x + 4y - 3) = 2 \times 0$$2×(x+4y−3)=2×0

$$2x + 8y - 6 = 0$$2x+8y−6=0

This is exactly the same as Equation 2.

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Both equations represent the same line, just written in different ways.

When two equations represent the same line, every point on that line satisfies both equations.

Since a line contains infinitely many points, there are infinite solutions.

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For equations $a_1x + b_1y + c_1 = 0$a1​x+b1​y+c1​=0 and $a_2x + b_2y + c_2 = 0$a2​x+b2​y+c2​=0:

$\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$a2​a1​​=b2​b1​​=c2​c1​​ indicates infinite solutions.

For the given equations:

$$\dfrac{1}{2} = \dfrac{4}{8} = \dfrac{-3}{-6} = \dfrac{1}{2}$$21​=84​=−6−3​=21​

Therefore, the equations have infinite solutions.