The sum of two numbers is 14 and the diference is 6 what are the two numbers?

2 Answers
Mar 11, 2018

a = 10 and b = 4.

Explanation:

Let a be the larger and b be the smaller. We know that

a+b = 14 and a-b = 6.

Solving the 2nd equation for a,

a = 6 + b.

Substituting that expression for a in for the a in the first equation, and then solving for b,

6+b+b = 14

2*b = 14-6 = 8

b = 8/2 = 4
Therefore a = 6+4 = 10.

I hope this helps,
Steve

Mar 11, 2018

10 and 4.

Explanation:

Let's call the two numbers x and y. We know that x+y=14 and x-y=6. We could guess and check, but there is an easier way. We can use elimination to solve for x and y, using *just these two equations! *


Why?
We can rewrite these two equations as 1x+1y=14 and 1x+(-1y)=6. Note that x's coefficients are the same, so we can subtract the equations and x will disappear, leaving us with the solution for y. Also note that y's coefficients are additive inverses, so we can add the equations and y will disappear, giving us the solution for x! That's both variables! Here we go:


Subtracting (solution for y):
cancel(x)+y=14
cancel(x)-y=6
y-(-y)=8 y+y=8 2y=8 y=4 **So, one of the numbers is 4#.**

Adding (solution for x)
xcancel(+y)=14
xcancel(-y)=6
2x=20
x=10
So, the other number is 10.


Let's check:
x+y=14
10+4=14
14=14


x-y=6
10-4=6
6=6
We're good!

So, the two numbers are 10 and 4.