Let's begin by listing out the information given to us:
[tex]\begin{gathered} 6x-48=-15y-----1 \\ 2x+5y=16-------2 \end{gathered}[/tex]We will solve these equation simultaneously following these steps:
I. We will pick a number to multiply the equation such that the values of corresponding variables are equal
[tex]\begin{gathered} 6x-48=-15y-----1 \\ 2x+5y=16-------2 \\ \text{Multiply equation 2 by 3, so we can eliminate the x variable} \\ 6x+15y=48------3 \\ \text{Combine equations 1 \& 3, we have:} \\ 6x-48=-15y-----1 \\ 6x+15y=48------3 \end{gathered}[/tex]II. Subtract equation 3 from 1, we have:
[tex]\begin{gathered} 6x-48=-15y-----1 \\ \operatorname{Re}arranging\text{ equation 1, we have:} \\ 6x+15y=48------1 \\ 6x+15y=48------3 \\ \text{Equation 1 - 3 is:} \\ 6x-6x+15y-15y=48-48 \\ 0+0=0\Rightarrow0 \end{gathered}[/tex]The solution for these equations is non-existent
