The sum of two numbers is 35. Their difference is 65.
1 answer:
We are given that the sum of two numbers is 35. If "x" and "y" are the numbers then this means mathematically the following:
Now we are told that this difference is 65, this can be expressed mathematically as:
Therefore, we have two equations and two variables. To solve this system we can add both equations together, in such a way that the variable "y" is eliminated, like this:
Solving the operations:
Dividing both sides by 2:
The first number is 50. Now we replace this number in equation (1):
Subtracting 50 to both sides:
The numbers are 50 and -15.
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The solution to this system is (x, y) = (8, -22).
The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).
You can extend each table after the same pattern.
In table 1, x-values increase by 2 and y-values decrease by 8.
In table 2, x-values increase by 2 and y-values decrease by 6.
The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...
... (x, y) = (8, -22)
