CUET UG 2025 — General Test Quantitative Reasoning

Given equations:

$2x + 3y - 8 = 0$2x+3y−8=0 ... (1)

$3x - 2y - 12 = 0$3x−2y−12=0 ... (2)

Rewriting:

$2x + 3y = 8$2x+3y=8 ... (1)

$3x - 2y = 12$3x−2y=12 ... (2)

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Multiply equation (1) by 2:

$$4x + 6y = 16$$4x+6y=16

Multiply equation (2) by 3:

$$9x - 6y = 36$$9x−6y=36

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Adding both equations:

$$4x + 6y = 16$$4x+6y=16

$$9x - 6y = 36$$9x−6y=36

$$13x = 52$$13x=52

$$x = 4$$x=4

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Substitute $x = 4$x=4 into equation (1):

$$2(4) + 3y = 8$$2(4)+3y=8

$$8 + 3y = 8$$8+3y=8

$$3y = 0$$3y=0

$$y = 0$$y=0

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Substitute $x = 4$x=4 and $y = 0$y=0 into $4x^2 + y^2 - 4x$4x2+y2−4x:

$$4x^2 + y^2 - 4x$$4x2+y2−4x

$$= 4(4)^2 + (0)^2 - 4(4)$$=4(4)2+(0)2−4(4)

$$= 4(16) + 0 - 16$$=4(16)+0−16

$$= 64 - 16$$=64−16

$$= 48$$=48

Therefore, $4x^2 + y^2 - 4x = 48$4x2+y2−4x=48.