The sum of two numbers is 78. Their difference is 32. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.

This is mathematics

System of equations:

x+y=78

x-y=32

Two numbers:

x=55 y=23

Explanation:

A system of equations has two equations that we can use to find both of the variables x and y. So, we need to create two equations that represent this situation.

The first part of the problem states that the sum of two numbers is 78. These two numbers are going to be x and y. Therefore, our first equation is

x+y=78

Our next portion of the question says that those two numbers we have established as x and y also have a difference of 32. Therefore, our second equation is

x-y=32

The system of equations looks like this:

x+y=78

x-y=32

Now, we need to solve by elimination. That means we need to line the equations up, like we already have, and add vertically. (If you‘re not familiar with this concept and you don’t understand what’s happening, there’s tons of videos online that can help explain better than me!)

x+y=78

x-y=32

2x=110  Divide both sides by 2.

x=55

Now we know one of the numbers, so all we have to do is plug x into one of the equations to get y! (I’m plugging it into the first equation so that I don‘t get a negative y.)

55+y=78  Subtract both sides by 55.

-55    -55

y=23

Finally, we have our two numbers. We can plug them into the equations just to make sure that they’re correct.

(55)+(23)=78

78=78

(55)-(23)=32

32=32

I hope this helped you out…have an amazing day :D

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