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

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

Solution:

2x + 3y = 11 (1)

2x – 4y = -24 (2)

From Equation (1), We obtain

\frac{11 - 3 y}{2}

(3)

By putting this value in equation (2), we obtain

(\frac{11 - 3 y}{2})

-4y = -24

11 – 3y – 4y = -24

-7y = -35

y = 5 (4)

Putting this value in equation (3), we obtain

\frac{11 - 3 \times 5}{2} = \frac{- 4}{2} = - 2

Hence, X=-2, y=5

y=mx+3

5=m(-2) + 3

5 – 3 = m(-2)

2 = m (-2)

m = -1 Ans