the sum of two is 4 and their difference is 0

Question

Whats the answer to this?

Answer 1

The SUM of TWO NUMBERS is 4 and THEIR DIFFERENCE is ZER0.

x +y = 4

x-y = 0

Adds the equations together... 2x = 4 ---> x = 2 then y=2

2+2=4 and 2-2=0

Answer 2

This is listed under elementary math. Are you working with variables yet? ("Variables" are letters, like x and y, used to replace numbers in pre-algebra and algebra.) If you are, check out the answers other tutors gave.

If not, here's how to solve the problems without variables!

Step 1. Think of all the combinations you can that add up to four. To simplify it, let's start by using just positive numbers and zero.

0+4

1+3

2+2

3+1

4+0

And.... stop! That's it. Those are all the combinations of non-negative numbers that add up to four.

Step 2. Let's take out any number combinations that are repeats. For example, 0+4 is the same as 4+0, and 1+3 is the same as 3+1.

0+4

1+3

2+2

3+1

4+0

That leaves:

0+4

1+3

2+2

Step 3. Let's do subtraction with each of these pairs, and see which gives us zero.

0 - 4 = -4

4 - 0 = 4

So it's not 0, 4!

1 - 3 = -2

3 - 1 = 2

So it's not 1, 3!

2 - 2 = 0

So that's it!

Solution: 2+2=4, and 2-2=0. The answer is 2 and 2.

Answer 3

Steps using Substitution – To solve a pair of equations using Substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

X + Y = 4 , X – Y = 0

X + Y = 4

X = - Y + 4

- Y + 4 – Y = 0

- 2Y + 4 = 0

- 2Y = - 4

Y = 2

X = -2 + 4

X = 2 , Y = 2

Steps using Elimination – In order to solve by Elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

X + y = 4 , x – y = 0

X – X + Y + Y = 4

Y + Y = 4

2Y = 4

Y = 2

X – 2 = 0

X = 2

X = 2 , Y = 2

Answer 4

Let x and y be the two numbers

x + y = 4

x - y = 0

Add the two equations together

2x = 4

solve for x

x = 2

Since x + y = 4 and x = 2, then y = 2

check: 2 + 2 = 4

2 - 2 = 0