Lesson 65: Advanced Substitution

We have used substitution to solve systems of equations that are derived from uniform motion word problems. In the systems studied thus far, such as R T + 210 = R T R = 4 R = 6 T + T = 5 The values of two of the variables have always been given. W W R R W R R W

Now we will investigate the solution of a system of four equations in which none of the values of the variables is given. In a later lesson, we will find that these equations will permit the solution of a new type of uniform motion problem. In the problem sets the problems of this type will be exactly like the two problems that we will work here. The numbers and the subscripts will change, but otherwise the problems will be the same.

Find the values of all four variables in this system of equations. Example: Find the values of all four variables in this system of equations. R T = 6 R = 3R T = 2 – T W W B B B W B W

Answer: R = 4 R = 12 T = 3/2 T = ½ W B

Find the values of all four variables in this system of equations. Example: Find the values of all four variables in this system of equations. R T = 693 R T = 165 R = 3R T + T = 12 P P C C P C P C

Answer: R = 33 R = 99 T = 7 T = 5 C P

HW: Lesson 65 #1-30