EquationsMCQPYQ Dec 22Question 992 of 221
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The solution of the following system of linear eqs. $2x - 5y + 4 = 0\displaystyle and $2x + y - 8 = 0 will be:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — (3,2)\displaystyle (3, 2)

All Options:

  • A(−2,3)\displaystyle (-2, 3)
  • B(1,−3)\displaystyle (1, -3)
  • C(3,2)\displaystyle (3, 2)
  • D(−2,2)\displaystyle (-2, 2)

Detailed Solution & Explanation

The given system of linear equations is: 2x−5y+4=0— (Equation 1)2x - 5y + 4 = 0 \quad — (Equation 1)\displaystyle \text{--- (Equation 1)} 2x+y−8=0— (Equation 2)2x + y - 8 = 0 \quad — (Equation 2)\displaystyle \text{--- (Equation 2)} From Equation 2, we can express y\displaystyle y in terms of x\displaystyle x: y=8−2x— (Equation 3)y = 8 - 2x \quad — (Equation 3)\displaystyle \text{--- (Equation 3)} Substituting Equation 3 into Equation 1: 2x−5(8−2x)+4=02x - 5(8 - 2x) + 4 = 0 2x−40+10x+4=02x - 40 + 10x + 4 = 0 12x−36=012x - 36 = 0 12x=36  ⟹  x=312x = 36 \implies x = 3 Substituting x=3\displaystyle x = 3 back into Equation 3: y=8−2(3)=8−6=2y = 8 - 2(3) = 8 - 6 = 2 Thus, the solution is (x,y)=(3,2)\displaystyle (x, y) = (3, 2). Hence, **Option C** is the correct answer.

About This Chapter: Equations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Linear, Quadratic and Cubic Equations

This chapter covers Linear, Quadratic and Cubic Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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The cost of 2\displaystyle 2 oranges and 3\displaystyle 3 apples is $28$. If the cost of an apple is doubled then the cost of $3orangesand\displaystyle oranges and5$ apples is $75$. The original cost of 7\displaystyle 7 oranges and 4\displaystyle 4 apples (in Rs) is:

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