SOLUTION: The sum of two numbers is 34. Their difference is 10. What are the two numbers?

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Question 44442This question is from textbook Begining Algebra
: The sum of two numbers is 34. Their difference is 10. What are the two numbers? This question is from textbook Begining Algebra

Found 3 solutions by stanbon, atif.muhammad, tutorcecilia:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 34. Their difference is 10. What are the two numbers?
x+y=34
x-y=10
Add to get 2x=44, then x=22 and y=12
Cheers,
stan H.
Answer by atif.muhammad(135)   (Show Source): You can put this solution on YOUR website!
Let one number be x, and the other number be y.

x and y

Their sum = 34

x + y = 34

Their difference = 10

x - y = 10

A little angel told me, the answer is 22 and 12!

We have a pair of simultaneous equations and will solve these using substitution. 

x + y = 34 (1)
x - y = 10 (2)

Rearrange (2):

x - y = 10

x = 10 + y (3)

Substitute (3) into (1)

x + y = 34

(10 + y) + y =34

10 + y + y = 34

2y = 24

y =12 (4)

Substitute (4) into (3)

x = 10 + y

x = 10 + 12 = 22

Hence the two numbers are 12, and 22.
Answer by tutorcecilia(2152)   (Show Source): You can put this solution on YOUR website!
Use x and y because we do not know the value of either number.
(x)+(y)=34 because the "sum" means to add.
(x)-(y)=10 because the "difference" means to subtract.
.
Solve using either the substitution or addition method for solving systems of linear equations:
.
-(x+y=34)
+(x-y=10)
_________

.
.
-x-y=-34
+x-y=+10
_________
0-2y=-24
.
.
Solve for y:
-2y=-24
-y=-24/2
y=12
.
.
Plug y=12 back into the original equations and solve for x:
x+y=34
x+12=34
x+12-12=34-12
x=22
.
x-y=10
x-12=10
x-12+12=10+12
x=22
.
.
Checking that x=22 and y=12:
22+12=34
22-12=10
The values check out.

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