Respuesta :
Answer: The two numbers are 28 and 21
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Explanation:
Let x and y be the unknown numbers.
The two equations we're dealing with are
[tex]\begin{cases} x-y = 7\\ x+y = 49\\ \end{cases}[/tex]
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.
