The sum of two numbers is 38. Their difference is 12. What are the two numbers?
x=one number
y=other number
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x+y=38
x-y=12
Solve for x and y.
The easiest way to start is to add the two equation which will elminate the y variable and you can solve for x.
To find the two numbers, let's create a system of equations using the given information.
Let's assume the first number is x and the second number is y.
According to the problem, the sum of two numbers is 38, so we can write the equation:
x + y = 38 -- Equation 1
Also, the difference between the two numbers is 12, so we can write another equation:
x - y = 12 -- Equation 2
Now we have two equations which are Equation 1 and Equation 2.
To find the values of x and y, we can solve this system of equations using the method of substitution or elimination.
Let's solve this system using the method of elimination:
Multiply Equation 1 by -1, so that the coefficients of y are the same, but with opposite signs:
-1(x + y) = -1(38)
- x - y = -38 -- Equation 3
Now let's add Equation 2 and Equation 3:
(x - y) + (- x - y) = 12 + (-38)
-2y = -26
Divide both sides by -2:
-2y / -2 = -26 / -2
y = 13
Now, substitute the value of y in Equation 1 (x + y = 38):
x + 13 = 38
Subtract 13 from both sides:
x + 13 - 13 = 38 - 13
x = 25
So the two numbers are 25 and 13.