sum of two numbers is 42.Their difference is 6.What are the two numbers?
X+Y=42
X-Y=6
2X=48
24+18=42
24-18=6
To find the two numbers, we can use a system of equations. Let's assign variables to the two numbers:
Let x be the first number.
Let y be the second number.
From the given information, we can set up two equations:
Equation 1: x + y = 42 (The sum of the two numbers is 42)
Equation 2: x - y = 6 (The difference between the two numbers is 6)
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution Method
Let's solve Equation 1 for x and substitute it into Equation 2:
x = 42 - y (Substitute the value of x from Equation 1 into Equation 2)
Now we can substitute this value of x into Equation 2:
(42 - y) - y = 6 (Replace x in Equation 2 with (42 - y))
Simplifying Equation 2:
42 - 2y = 6 (Combine like terms: -y - y = -2y)
Let's solve Equation 2 for y:
-2y = 6 - 42 (Move 42 to the right side by subtracting)
-2y = -36 (Combine like terms: 6 - 42 = -36)
Divide both sides of the equation by -2:
y = (-36) / (-2) (Divide both sides of the equation by -2)
y = 18 (Simplify)
Now that we have found the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 18 = 42 (Replace y in Equation 1 with 18)
Subtract 18 from both sides of the equation:
x = 42 - 18 (Subtract 18 from both sides)
x = 24 (Simplify)
Therefore, the two numbers are x = 24 and y = 18.
So, the two numbers are 24 and 18.
x + y = 42
x - y = 6
2x = 48
x is the larger number.
Take it from there