Question

What is the solution to the following system of linear equations?

4y − 36 = −12x
3x + y = −9

Answer 1

Given system of linear equation 4y – 36 = -12x and 3x + y = -9 do not have any solution.

Solution:

Need to determine solution of following system of linear equations

4y – 36 = -12x

3x + y = -9

lets modify given equation in standard form

12x + 4y -36 = 0 -------(1)

3x + y + 9 = 0 -------(2)

Lets first analyze whether given system of equation is having solution or not.

`\text { If } a_(1) x+b_(1) y+c_(1)=0 \text { and } a_(2) x+b_(2) y+c_(2)=0` are two equation and
`\left((a_(1))/(a_(2))\right)=\left((b_(1))/(b_(2))\right) \text { not equal to }\left((c_(1))/(c_(2))\right)` then the given system of equation has no solution

In our case

`\begin{array}{l}{a_(1)=12, b_(1)=4 \text { and } c_(1)=-36} \\ {a_(2)=3, b_(2)=1, \text { and } c_(2)=9}\end{array}`

`\begin{array}{l}{(a_(1))/(a_(2))=(12)/(3)=4} \\\\ {(b_(1))/(b_(2))=(4)/(1)=4} \\\\ {(c_(1))/(c_(2))=-(36)/(9)=-4}\end{array}`

`(a_(1))/(a_(2))=(b_(1))/(b_(2))=4 \text { and not equal to } (c_(1))/(c_(2))=-4`

This is condition of no solution.

Hence given system of linear equation 4y – 36 = -12x and 3x + y = -9 do not have any solution.