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
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.
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.
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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