Question

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

[ 2 Marks ]

Answer 1

2x + 3y = 11 ...(i)
Subtracting 3y from both the sides, we get,
2x = 11 - 3y …(ii)
2x – 4y = - 24 …(iii)
Substituting the value of 2x in equation (iii), we get,
11- 3y - 4y = - 24
$\Rightarrow$ -7y = - 24 - 11
$\Rightarrow$ -7y = - 35
$\Rightarrow$ $y=\frac{-35}{-7}$
$\Rightarrow$ y = 5
[0.5 marks]

Substituting the value of y in equation (ii) we get
$2x=11-3\times 5$
$\Rightarrow$ 2x = 11- 15
$\Rightarrow$ 2x = - 4
Dividing by 2, we get;
$\Rightarrow$ x = - 2
[0.5 marks]

Substituting the value of x and y,
y = mx + 3.
5 = -2m +3
2m = 3 - 5
$m=\frac{-2}{2}$
m = -1
[1 mark]