Exercise 51 Page 384

When solving a system of equations using substitution, there are three steps.

1. Isolate a variable in one of the equations.
2. Substitute the expression for that variable into the other equation and solve.
3. Substitute this solution into one of the equations and solve for the value of the other variable. For this exercise, y is already isolated in one equation, so we can skip straight to solving.
   x-7=y & (I) 2x-y=41 & (II)

   RearrangeEqn

   (I): Rearrange equation

   y=x-7 2x-y=41

   Substitute

   (II):y= x-7

   y=x-7 2x-( x-7)=41

   Distr

   (II):Distribute -1

   y=x-7 2x-x+7=41

   SubTerm

   (II):Subtract term

   y=x-7 x+7=41

   SubEqn

   (II): LHS-7=RHS-7

   y=x-7 x=34

   Great! Now, to find the value of y, we need to substitute x for 34 into the first equation in the given system.

   y=x-7 x=34

   Substitute

   (I):x= 34

   y= 34-7 x=34

   SubTerm

   (I): Subtract term

   y=27 x=34

   The solution, or point of intersection, to this system of equations is the point (34,27).