Question

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

Answer 1

Step 1: Finding the expression of $x$ from equation $\left(I\right)$

The given equations are as follows.

$2x+3y=11\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots ..\left(I\right)$

$2x–4y=-24\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \left(II\right)$

$x=\frac{(11-3y)}{2}\dots \dots \dots \dots \dots \dots \dots .\left(III\right)\mathbf{}\left(\mathrm{from}\mathrm{equation}\left(I\right)\right)$

Step 2: Finding the value of $y$ by putting the value of $x$ in equatrion $\left(2\right)$

$2\frac{(11-3y)}{2}–4y=-24$

$\Rightarrow 11–3y–4y=-24$

$\Rightarrow -7y=-35$

$\Rightarrow y=5...\left(IV\right)$

Step 3: Putting the value of $y$ in equation $\left(III\right)$

$x=\frac{(11-3\times 5)}{2}$

$=\frac{-4}{2}$

$=-2$

Hence, $x=-2,y=5$

Step 4: Finding the value of $m$

Putting the value of $x$ and $y$ in the equation $y=mx+3$, we get

$5=\left(-2m\right)+3$

$5-3=-2m$

$2=-2m$

So, $m=-1$

Therefore the value of $m$ is $-1$.