Question

How can you solve problems involving equivalent expressions?

Answer 1

Setting expressions equal to one another gives us an equation.

In an equation, our goal is to isolate the variable; we must "undo" everything that has been done to the variable. We work backward; the last thing done to the variable will be the first thing we undo.

We "undo" things by performing the opposite operation; for instance, if the last thing done to our variable was that 3 was subtracted from it, we would undo that first by adding 3 to both sides.

What we do to one side we must do to the other in order to preserve equality.

We would continue this process of working backward until the variable was isolated; this would give us our solution.

Answer 2

Solution

Consider Case 1

Find cost of 4 pens and 5 pencils if cost of one pen is $ x and Cost of one pencil is $ y.

So, Total cost of 4 pens and 5 pencils is given by: Z= 4 x + 5 y

Case 2:

The cost of one kg of wheat is $ R and one kg of Rice Cost $ S.Find the total cost of 4 Kg of wheat and 5 Kg of rice.

So, Cost of 4 Kg of wheat and 5 Kg of rice,M= 4 R + 5 S

4 x + 5 y= 4 R + 5 S

As, in both the cases  , total cost ,Z as well as M are equivalent expressions.

So, as there are two variables in each case, as coefficient of variables being the same.

So, just substitute different integral or real values of variables ,and we will get the result according to given problem.