Q:

Classify the following system of equations.8x - 12y = -918x + 27y = 21

Accepted Solution

A:
The following system of equations 8x - 12y = -9   and 18x + 27y = 21 are intersecting linesSolution: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 [tex]x = \frac{3}{144} = \frac{1}{48}[/tex]Substitute "x" value in (2) [tex]\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}[/tex]So, given system of equations has 1 solution [tex]\left(\frac{1}{48}, \frac{55}{72}\right)[/tex] which means that, they are intersecting lines. Hence, the given system of equations are classified as intersecting lines