Find the difference of two numbers is 3 . Their sum is 13. Find the two numbers

Answer 1

the difference of two numbers is 3 is represented by: x - y = 3

their sum is 13 is represented by: x + y = 13

we now have a system of equations:

x - y = 3

x + y = 13

Using the elimination method the y's cancel out, add the remaining like terms to get:

2x = 16

divide by 2:

x = 8

Now substitute x = 8 back into either one of the original equations

x + y = 13

8 + y = 13

subtract 8 from both sides to get

y = 5

So the solution to the system is (8, 5)

x = 8 and y = 5

Answer 2

let x=1st number

let y=second number

The 2 equations would be:

x-y=3

x+y=13

Can solve by any method, I will show substitution. Solve the first equation for x by adding y to both sides

x-y+y=3+y Simplify

x=3+y

Substitute into the second equation

(3+y)+y=13 Combine like terms

3+2y=13 Subtract 3 from both sides

3+2y-3=13-3

2y/2=10/2

y=5 Can plug this into either equation and solve for x

x=3+y

x=3+5

x=8

The numbers are 5 and 8.

Answer 3

you want to write two equations to solve this, we call these simultaneous equations

the first is the difference of two numbers is 3

x - y = 3

the second is the sum equals 13

x+ y = 13

we can use the elimination method to solve for x and then subsequently solve for y

x - y = 3

x + y = 13

if we add these two equations the "y" goes away

2x = 16

dividing by 2 we get x = 8

If x is 8 we can use either of our original equations to solve for y

x - y = 3

8 - y = 3

therefore y = 5