Respuesta :
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:
[tex]\begin{gathered} 3x+6y=-18 \\ 2y=3x-22 \end{gathered}[/tex]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":
[tex]\begin{gathered} 2y=3x-22 \\ y=\frac{3x-22}{2} \end{gathered}[/tex]Now, we can substitute "y" into the other equations, that is, the first one:
[tex]\begin{gathered} 3x+6y=-18 \\ 3x+6\frac{(3x-22)}{2}=-18 \end{gathered}[/tex]Now, the equations has only "x", so we can solve for it:
[tex]\begin{gathered} 3x+3(3x-22)=-18 \\ 3x+9x-66=-18 \\ 12x=-18+66 \\ 12x=48 \\ x=\frac{48}{12} \\ x=4 \end{gathered}[/tex]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:
[tex]\begin{gathered} 2y=3x-22 \\ 2y=3\cdot4-22 \\ 2y=12-22 \\ 2y=-10 \\ y=-\frac{10}{2} \\ y=-5 \end{gathered}[/tex]So, the solution of the given system of equations is x = 4 and y = -5.
