the sum of two numbers is 21 and their difference is 13. find two numbers
x + y = 21
x - y = 13
Solve the system ... adding the equations will cancel the y.
x+y=21
x-y=13
To find the two numbers, we can solve the following system of equations:
Let's say the first number is x and the second number is y.
Equation 1: x + y = 21 (Since the sum of the two numbers is 21).
Equation 2: x - y = 13 (Since the difference between the two numbers is 13).
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution:
From Equation 2, we can isolate x by adding y to both sides:
x = 13 + y
Now substitute this value of x into Equation 1:
(13 + y) + y = 21
Simplify the equation:
13 + 2y = 21
Subtract 13 from both sides:
2y = 8
Divide both sides by 2:
y = 4
Now substitute the value of y back into Equation 1:
x + 4 = 21
Subtract 4 from both sides:
x = 17
So, the two numbers are x = 17 and y = 4.