Answer: The two numbers are 28 and 21
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Step-by-step explanation:
Let x and y be the unknown numbers.
The two equations we're dealing with are
The first equation talks about the difference being 7, and the second equation says their sum is 49. It's implied that x > y.
Add the equations straight down.
- The x terms add to 2x
- The y terms add to 0y, and go away
- The constants add to 7+49 = 56
We're left with 2x = 56 which solves to x = 28. Divide both sides by 2 to isolate x fully.
Then use this x value to find y. Pick on any equation with x and y in it.
Let's say we picked the first equation
x-y = 7
28-y = 7
-y = 7-28
-y = -21
y = 21
Or you could pick the second equation
x+y = 49
28+y = 49
y = 49-28
y = 21
Either way, we end up with the same y value.
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As a check:
x-y = 28-21 = 7
x+y = 28+21 = 49
The answers are confirmed.