Question 6 of 9intermediate🔧 ApplyShort Answer2 marks

Solve 2x+3y=112x + 3y = 11 and 2x−4y=−242x - 4y = -24 and hence find the value of ‘mm’ for which y=mx+3y = mx + 3.

Correct Answer

x = -2, y = 5 and m = -1

Exercise: EXERCISE 3.2 | Q: 2 | (Page Page 10)
For More Understanding

Explanation

This question tests the student's ability to solve a pair of linear equations using elimination or substitution method, and then use the solution to find an unknown parameter. The textbook demonstrates both methods in Exercise 3.2 and 3.3.

Solution Steps

  1. Step 1: Given equations are 2x + 3y = 11 ...(1) and 2x - 4y = -24 ...(2). Subtracting equation (2) from equation (1): (2x + 3y) - (2x - 4y) = 11 - (-24), we get 7y = 35, therefore y = 5.

  2. Step 2: Substituting y = 5 in equation (1): 2x + 3(5) = 11, we get 2x + 15 = 11, therefore 2x = -4 and x = -2.

  3. Step 3: For y = mx + 3, substituting x = -2 and y = 5: 5 = m(-2) + 3, we get 5 = -2m + 3, therefore -2m = 2 and m = -1.

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