Question

Solve 2x + 3y = 11 and 2x − 4y = −24 and hence find the value of 'm' for which y = mx + 3
(a) 3
(b) -4
(c) -1
(d) 5

Answer 1

Hint: First, solve the given pair of linear equations by subtracting equation (2) from equation (1) to get y = 5. Substitute this to equation (1) to get x = -2. Substitute x = -2 and y = 5 into y = mx + 3 and solve for m to get the final answer.

Complete step-by-step answer:
In this question, we need to solve the two given equations: 2x + 3y = 11 and 2x − 4y = −24 and then use this solution set to find the value of m for which y = mx + 3.

The given pair of linear equations are:

2x + 3y = 11 …(1)

2x − 4y = −24 …(2)

Subtracting equation (2) from equation (1), we will get the following:

$\Rightarrow$ 2x + 3y – (2x – 4y) = 11 – (-24)

$\Rightarrow$ 2x + 3y – 2x + 4y = 11 + 24

$\Rightarrow$ 7y = 35

$\Rightarrow$ y = 5

Now, substituting this y = 5 in equation (1), we will get the following:

$\Rightarrow$ 2x + 3y = 11

$\Rightarrow$ 2x + 3(5) = 11

$\Rightarrow$ 2x + 15 = 11

$\Rightarrow$ 2x = - 4

$\Rightarrow$ x = -2

So, we have the solution set for the given pair of linear equations: x = -2 and y = 5.

Now, we need to find the value of m which satisfies y = mx + 3.

Substituting, x = -2 and y = 5 into y = mx + 3, we will get the following:

$\Rightarrow$ 5 = -2m + 3

$\Rightarrow$ 2 = -2m

$\Rightarrow$ m = -1

So, option (c) is correct.

Note: In this question, it is very important to know how to solve a pair of linear equations. In the above solution, we subtracted one equation by the other to eliminate one variable. We can also solve a pair of linear equations by taking one equation and expressing one variable in terms of the other. Substitute this expression in the other equation to eliminate one variable. Then solve in the same way as done in the above solution.