Question

Solve 2x + 3y = 11 and x − 2y = −12 algebraically and hence find the value

of ‘m’ for which y = mx + 3.

3​

Answer 1

$\huge\underbrace\mathfrak\color{lime}{ †\: Question:–}$

2x + 3y = 11 and x - 2y = -12 and hence find the value of 'm' for which y = mx + 3

$\huge\underbrace\mathfrak\color{lime}{ †\: Answer:–}$

$~~~~~~~~~~~\huge\longrightarrow$$\bold{2x + 3y = 11}$ -------(1)

$~~~~~~~~~~~\huge\longrightarrow$$\bold{x - 2y = - 12}$ -------(2)

From equation (2) We have ;

$~~~~~~~~~~~~\longrightarrow$$\bold{x - 2y = - 12}$

$~~~~~~~~~~~~\longrightarrow$$\bold{x = - 12 + 2y}$ --------(2)

Substitute eq(3) in eq(1)

$~~~~~~~~~~~~\longrightarrow$$\bold{2x + 3y = 11}$

$~~~~~~~~~~~~\longrightarrow$$\bold{2( -12 + 2y) + 3y = 11}$

$~~~~~~~~~~~~\longrightarrow$$\bold{ - 24 + 4y + 3y = 11}$

$~~~~~~~~~~~~\longrightarrow$$\bold{7y = 11 + 24}$

$~~~~~~~~~~~~\longrightarrow$$\bold{7y = 35}$

$~~~~~~~~~~~~\longrightarrow$$\bold{y = \frac{35}{7}}$

$~~~~~~~~~~~~\longrightarrow$$\bold{y = 5}$

Substitute y = 5 in eq(3)

$~~~~~~~~~~~~\longrightarrow$$\bold{x = -12 + 2(5)}$

$~~~~~~~~~~~~\longrightarrow$$\bold{x = -12 + 10}$

$~~~~~~~~~~~~\longrightarrow$$\bold{x = - 2}$

The solution is y = 5 and x = - 2

$~~~~~~~~~~~~~y = mx + 3$

$~~~~~~~~~~~~\longrightarrow$$\bold{5 = m(-2) + 3}$

$~~~~~~~~~~~~\longrightarrow$$\bold{5 = -2m + 3}$

$~~~~~~~~~~~~\longrightarrow$$\bold{5 - 3 = - 2m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{2 = - 2m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{\frac{2}{-2} = m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{\cancel\frac{2}{-2} = m}$

$~~~~~~~~~~~~\longrightarrow$$\bold{m = - 1}$

So the answer for the solution y = mx + 3 Is

m = - 1