Exercise 10 Page 242

In this system of equations, at least one of the variables has a coefficient of 1. Therefore, we will approach its solution with the Substitution Method. 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.We have been given the following system of equations. x-y=1 & (I) x-y=6 & (II) Let's start by isolating the x variable in Equation (I). x-y=1 ⇔ x=1+y Now that we've isolated x, we can solve the system by substitution.
   x=1+y & (I) x-y=6 & (II)

   Substitute

   (II):x= 1+y

   x=1+y 1+y-y=6

   SubTerm

   (II):Subtract term

   x=1+y 1≠6
   Solving this system of equations resulted in a contradiction; 1 can never be equal to 6. The lines are parallel and do not have a point of intersection. Therefore, the system does not have a solution.