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

Explanation

We will use the elimination method to solve for x and y.

• Equation 1: 2x + 3y = 11
• Equation 2: 2x - 4y = -24

First, multiply Equation 1 by 2 to match the coefficients of x in both equations:

(2x + 3y = 11) × 2 → 4x + 6y = 22 (Equation 3)

Now subtract Equation 2 from Equation 3:

(4x + 6y) - (2x - 4y) = 22 - (-24)

4x + 6y - 2x + 4y = 46

(4x - 2x) + (6y + 4y) = 46

2x + 10y = 46

2x = 46 - 10y (Equation 4)

x = 23 - 5y (Equation 5)

Substitute x = 23 - 5y into Equation 1:

2(23 - 5y) + 3y = 11

46 - 10y + 3y = 11

46 - 7y = 11

-7y = 11 - 46

-7y = -35

y = 5

Step 2: Find the value of x

Now that we have y = 5, substitute it into Equation 1 to find x:

2x + 3(5) = 11

2x + 15 = 11

2x = 11 - 15

2x = -4

x = -2

Now, we are asked to find the value of 'm' for which y = mx + 3. We have the values x = -2 and y = 5. Substitute these into the equation y = mx + 3:

5 = m(-2) + 3

5 = -2m + 3

5 - 3 = -2m

2 = -2m

m = -1

Final Answer:

The value of m is -1.