Let's begin by listing out the information given to us:
[tex]\begin{gathered} x—5y=-3----1 \\ y=-4x-33---2 \end{gathered}[/tex]
In substitution method, we make one of the unknown variables to be the subject of the formula. In this case, we already have equation 2 in this form:
[tex]y=-4x-33[/tex]
We then substitute that variable into the other equation (equation 1), so that the new equation is expressed in only one variable rather than two variables:
[tex]\begin{gathered} x-5y=-3 \\ But,y=-4x-33 \\ x-5(-4x-33)=-3 \\ x+20x+165=-3 \\ 21x+165=-3 \\ Add,^{\prime}-165^{\prime}\text{ to both sides, we have:} \\ 21x+165-165=-3-165 \\ 21x=-168 \\ Divide\text{ both sides by 21, we have:} \\ \frac{21x}{21}=\frac{-168}{21}=-8 \\ x=-8 \\ \\ But,y=-4x-33 \\ But,x=-8 \\ y=-4(-8)-33\Rightarrow32-33=-1 \\ y=-1 \end{gathered}[/tex][tex](x,y)=(-8,-1)[/tex]
