Apply the given information to the equation and only look at one scenario at a time.
a-b=1,c=0 and a≠b, c=0
Practice makes perfect
We want to choose which of the given scenarios makes it so that the equation has only one solution. Beore we look at the options, notice that we can factor out x from the expression on the right-hand side.
c=ax-bx ⇕
c=(a-b)x
We also know that a, b, and c are whole numbers which means that they are always non-negative. Let's analyze each case, one at a time.
a-b=1,c=0
Let's focus on the first case.
Using this information, we can substitute 0 for c and 1 for a-b.
We end with an expression that tells us that c is equal to 0. However, based on the given information we know that it is not true because we are told that that c≠0. This means that these values of a, b, and c result in an equation that has no solution.
a=b,c=0
Now we will use information for the third case.
As with the previous case, we can substitute a for b in the equation since they are equal to each other. Additionally we can substitute 0 for c.
This time we end with an expression that is true for every value of the variable. Therefore, using this set of information we get an equation that has infinitely many solutions.
a≠b,c=0
Finally, let's focus on the last scenario.
We can substitute 0 for c. Additionally, since a≠b, the value of a-b is a non-zero value and we can divide by it.
