EIV (3rd Edition) Chapter 1 Question 10

[krajyk]

The problem asks to see if you can solve for X on 3 equations. The solution is to make all three equations have the same coefficient for X and determine if the coefficients for the other variables are different. How different do the coefficients need to be? In this example all were different but what if one had the same. For example, if 9a + 9b + 9x = 729 and 9a + 3b + 9x = 200, since 9a is repeated across two equations, would that means you can solve for X? Is there a general rule on what it means to have different coefficients?

[JonathanSchneider]

In your example we have a different coefficient for the second variable, b. As a result we can see that 6b = 529. (Simply subtract the second equation from the first.) Thus, b = some number. Now, we can put that number back into each of the two equations, but we will still have the same coefficients for a and x. As a result,w e cannot solve for those two variables.