Solve 2x + 3y =11 and 2x - 4y = - 24, and hence find the value of ‘m’ for which y = mx + 3.

Solution:

Solve the linear equations given by substitution method and substitute the values of x and y in y = mx + 3 to get the value of m.

2x + 3y = 11 ...(1)

2x - 4y = - 24 ...(2)

By solving equation (1)

2x + 3y = 11

3y = 11 - 2x

y = (11 - 2x) / 3 ...(3)

Substituting y = (11- 2x) / 3 in equation (2), we get

2x - 4[(11- 2x) / 3] = - 24

(6x - 44 + 8x) / 3 = - 24

14x - 44 = - 72

14x = 44 - 72

x = - 28/14

x = - 2

Substituting x = - 2 in equation (3)

y = [11 - 2 × (-2)] / 3

y = (11 + 4) / 3

y = 15/3

y = 5

Now, Substituting x = - 2 and y = 5 in y = mx + 3

y = mx + 3

5 = m(- 2) + 3

5 - 3 = - 2m

2 = - 2m

m = 2/(-2)

m = - 1

Thus, x = - 2, y = 5, and m = -1

☛ Check: NCERT Solutions Class 10 Maths Chapter 3

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Video Solution:

Solve 2x + 3y =11 and 2x - 4 y = -24, and hence find the value of ‘m’ for which y = mx + 3

NCERT Solutions for Class 10 Maths - Chapter 3 Exercise 3.3 Question 2

Summary:

On solving the pair of equations that are 2x + 3y =11 and 2x - 4 y = -24 the value of ‘m’ for which y = mx + 3 is -1.

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