The sum of two numbers is 6. The result when the greater number is decreased by twice the lesser is 9. Let x be the greater number and y be the lesser number. Find the numbers.
Thank you
x > y
x + y = 6
x - 2 y = 9
------------subtract
0 + 3 y = -3
y = -1
x = 7
To solve this problem, we can set up a system of two equations. Let's start by defining the variables:
x = the greater number
y = the lesser number
1) The sum of two numbers is 6:
x + y = 6
2) The result when the greater number is decreased by twice the lesser is 9:
x - 2y = 9
Now, we have two equations:
x + y = 6 (Equation 1)
x - 2y = 9 (Equation 2)
We can solve this system of equations using the method of substitution or elimination. Let's use the substitution method:
From Equation 1, we have:
x = 6 - y
Substitute this value of x into Equation 2:
6 - y - 2y = 9
Simplifying, we get:
-3y + 6 = 9
-3y = 3
y = -1
Now, substitute the value of y back into Equation 1 to find x:
x + (-1) = 6
x - 1 = 6
x = 7
Therefore, the greater number (x) is 7 and the lesser number (y) is -1.
So, the numbers are 7 and -1.