Quantitative Reasoning

Linear Equation

Medium

If 2x + 3y - 8 = 0 and 3x - 2y - 12 = 0, then $4x^2 + y^2 - 4x$ is equal to:

-48

✅ Correct Option: 4

Given equations:

$2x + 3y - 8 = 0$ ... (1)

$3x - 2y - 12 = 0$ ... (2)

Rewriting:

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

$3x - 2y = 12$ ... (2)

Multiply equation (1) by 2:

$4x + 6y = 16$

Multiply equation (2) by 3:

$9x - 6y = 36$

Adding both equations:

$4x + 6y = 16$

$9x - 6y = 36$

$13x = 52$

$x = 4$

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

$2(4) + 3y = 8$

$8 + 3y = 8$

$3y = 0$

$y = 0$

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

$4x^2 + y^2 - 4x$

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

$= 4(16) + 0 - 16$

$= 64 - 16$

$= 48$

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

2025: 24 May Shift 2

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A. 20

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C. 40

D. 50

Choose the correct answer from the options given below:

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If 2x + 3y - 8 = 0 and 3x - 2y - 12 = 0, then 4x2+y2−4x4x^2 + y^2 - 4x4x2+y2−4x is equal to:

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)

If 2x + 3y - 8 = 0 and 3x - 2y - 12 = 0, then $4x^2 + y^2 - 4x$ is equal to: