Graphical methods, solutions, applications MCQs

Q1. For what value of k does the equation kx + 2y = 5 have (1, 2) as a solution?

• A.1
• B.2
• C.−1
• D.5

Answer: A. 1

Start by listing the data - 2, 5, 1, 2 (math, chapter 'Linear Equations in Two Variables'). What we must find: the requested quantity. The principle that connects these is - k(1) + 2(2) = 5 ⇒ k + 4 = 5 ⇒ k = 1. Substituting and simplifying: k(1) + 2(2) = 5 ⇒ k + 4 = 5 ⇒ k = 1. That lands on option A) 1.

Q2. The point (3, −4) lies on which of these lines?

• A.2x + y = 2
• B.x + y = 1
• C.x − y = 1
• D.3x + 4y = 0

Answer: A. 2x + y = 2

Reading the problem, 3, 4 (math, chapter 'Linear Equations in Two Variables'). Our target: the unknown asked. The principle that connects these is - Check 2x + y at (3,−4): 6 + (−4) = 2. The arithmetic is: Check 2x + y at (3,−4): 6 + (−4) = 2. That lands on option A) 2x + y = 2.

Q3. The line y = 3x − 5 passes through which of the following points?

• A.(2, 1)
• B.(2, 0)
• C.(0, 5)
• D.(1, 3)

Answer: A. (2, 1)

The problem states: 3; 5. We need: the unknown asked in the stem. Formula - Check (2,1): 3(2) − 5 = 1. This is the equation that links the given quantities to the unknown (math, chapter 'Linear Equations in Two Variables'). Numerically: Check (2,1): 3(2) − 5 = 1. What makes this the correct method - ✓ It passes through (2,1). Consequently the answer is A) (2, 1).