Question

Classify the following system of equations. 8x - 12y = -9 18x + 27y = 21

Answer 1

The following system of equations 8x - 12y = -9   and 18x + 27y = 21 are intersecting lines

Solution:

Given, system of equations are 8x – 12y = - 9 ⇒ (1)

And 18x + 27y = 21 ⇒ 6x + 9y = 7 ⇒ (2)

We have to classify the above given system of equations  

For the we have to find the solution for the given system of equations

So, now, multiply (1) with 9 and (2) with 12, such that both equations will have same coefficients for y terms, such that, it will be easier to find solution while calculations by cancelling.

72x – 108y = - 81

72x + 108y = 84

(+) ---------------------------

144x + 0y = 3

144x = 3

$x = \frac{3}{144} = \frac{1}{48}$

Substitute "x" value in (2)

$\begin{array}{l}{\rightarrow 6\left(\frac{1}{48}\right)+9 y=7} \\\\ {\rightarrow \frac{1}{8}+9 y=7} \\\\ {\rightarrow 1+72 y=56} \\\\ {\rightarrow 72 y=55} \\\\ {\rightarrow y=\frac{55}{72}}\end{array}$

So, given system of equations has 1 solution $\left(\frac{1}{48}, \frac{55}{72}\right)$ which means that, they are intersecting lines.

Hence, the given system of equations are classified as intersecting lines