Question

A cord is cut into two pieces of different lengths. the sum of the two lengths is 10 centimeters, and the difference between the two lengths is 4 centimeters. find the lengths of the two pieces of cord.

Answer 1

Start with x+y=10 and x-y=4

Add the equations to eliminate y:

x+y=10

+ x-y=4

2x =14

So now solve for x:

2x=14 (Divide each side by 2 to get x by itself)

x=7

Now you have solved for x, but you still need to solve for y:

x+y=10

7+y=10 (Subtract 7 from both sides to get y by itself)

y=3

Now you have both x and y but to check it, just plug it into the original equations:

x+y=10 ----> 7+3=10 (That's correct)

x-y=4 ----> 7-3=4 (That's correct)

Explanation:

Answer 2

Start with x+y=10 and x-y=4
Add the equations to eliminate y:
x+y=10
+ x-y=4
2x =14
So now solve for x:
2x=14 (Divide each side by 2 to get x by itself)
x=7
Now you have solved for x, but you still need to solve for y:
x+y=10
7+y=10 (Subtract 7 from both sides to get y by itself)
y=3
Now you have both x and y but to check it, just plug it into the original equations:
x+y=10 ----> 7+3=10 (That's correct)
x-y=4 ----> 7-3=4 (That's correct)
There's your final answer.