We are given the following system of equations:
[tex]\begin{gathered} -9x-5y=-18,\text{ (1)} \\ 4x+5y=33,\text{ (2)} \end{gathered}[/tex]We are asked to solve the system, to do that we can solve for "y" in equation (1), and replace that value in equation (2), like this.
[tex]-9x-5y=-18[/tex]adding 9x on both sides
[tex]\begin{gathered} -9x+9x-5y=-18+9x \\ -5y=-18+9x \end{gathered}[/tex]dividing by -5 on both sides:
[tex]y=\frac{-18+9x}{-5}[/tex]replacing this value of "y" in equation (2) we get:
[tex]\begin{gathered} 4x+5y=33 \\ 4x+5(\frac{-18+9x}{-5})=33 \end{gathered}[/tex]Simplifying we get:
[tex]4x+18-9x=33[/tex]adding like terms:
[tex]-5x+18=33[/tex]subtracting 18 on both sides
[tex]\begin{gathered} -5x+18-18=33-18 \\ -5x=15 \end{gathered}[/tex]dividing by -5 on both sides:
[tex]x=\frac{15}{-5}=-3[/tex]Now we can find the value of "y" replacing the value of "x" that we have found, like this:
[tex]y=\frac{-18+9x}{-5}[/tex][tex]y=\frac{-18+9(-3)}{-5}[/tex]Solving the operations:
[tex]y=\frac{-18-27}{-5}=\frac{-45}{-5}=9[/tex]Therefore, the solution of the system is x = -3 and y = 9
