Exercise 37 Page 248

To begin, if $x=\text{-}3$ is in fact a solution to the equation it means we can substitute $x=\text{-}3$ into the equation and it will make a true statement. To determine the necessary values of $m$ and $b,$ we will hence begin by substituting $x=\text{-}3$ into the equation and simplify. At this point, our equation is $\text{-}3m+b=5.$ We can now arbitrarily choose the value of one of the variables. For example, if we let $m=1$ we can find the corresponding value of $b.$ Thus, if $m=1$ then $b=8.$ Let's write our equation with those values. By graphing the lines $y=x+8$ and $y=\text{-}2x-1$ we can make sure that the $x\text{-}$coordinate of the intersection point is $x=\text{-}3.$

The lines intersect at $(\text{-}3,5),$ which means the solution to the equation is in fact $x=\text{-}3.$