Question

I need help understanding solving linear systems by substitution:3x + 6y = -182y = 3x - 22

Answer 1

The basic concept of solving a system of equations using substitution is:

- solve for one of the variables in one of the equations

- substitute this into the other equation and solve for the remaining variable

- substitute the variable you found into either equations to find the other variable.

The system of equations is:

`\begin{gathered} 3x+6y=-18 \\ 2y=3x-22 \end{gathered}`

We can see that in the second equation "y" is almost solved, we just need to pass the "2" to the other side, so let's use this equations a solve for "y":

`\begin{gathered} 2y=3x-22 \\ y=(3x-22)/(2) \end{gathered}`

Now, we can substitute "y" into the other equations, that is, the first one:

`\begin{gathered} 3x+6y=-18 \\ 3x+6((3x-22))/(2)=-18 \end{gathered}`

Now, the equations has only "x", so we can solve for it:

`\begin{gathered} 3x+3(3x-22)=-18 \\ 3x+9x-66=-18 \\ 12x=-18+66 \\ 12x=48 \\ x=(48)/(12) \\ x=4 \end{gathered}`

And now that we know that x = 4, we can substitute this into any of the two equations. Let's do it in the second:

`\begin{gathered} 2y=3x-22 \\ 2y=3\cdot4-22 \\ 2y=12-22 \\ 2y=-10 \\ y=-(10)/(2) \\ y=-5 \end{gathered}`

So, the solution of the given system of equations is x = 4 and y = -5.