Question

Solve the following using substitution: 3X = 6Y -44X + 3Y = -1

Answer 1

We need to solve the system:

`\begin{gathered} 3x=6y-4 \\ 4x+3y=-1 \end{gathered}`

The first step is to isolate one of the variables and replace it at the other equation. We will isolate the "x" variable on the first equation:

`x=(6y)/(3)-(4)/(3)`

Then we replace this value on the second equation:

`\begin{gathered} 4\cdot((6y)/(3)-(4)/(3))+3y=-1 \\ (24y)/(3)-(16)/(3)+3y=-1 \\ (24y-16+9y)/(3)=-1 \\ 33y-16=-3 \\ 33y=-3+16 \\ 33y=13 \\ y=(13)/(33) \end{gathered}`

We can use this value to determine x.

`\begin{gathered} x=(6\cdot(13)/(33))/(3)-(4)/(3) \\ x=((78-132)/(33))/(3)=((-54)/(33))/(3)=(-54)/(99)=(-18)/(33)=(-6)/(11) \end{gathered}`

The solution to the system is (-6/11, 13/33)