Find the numbers whose sum is 15, if twice the first number minus the second number equals 6.
7 + 8
6 + 9
5 + 10
4 + 11
3 + 12
2 + 13
1 + 14
Which of those combination meets the second part of your question?
6+9
6,9
To find the numbers whose sum is 15, while also satisfying the given condition of "twice the first number minus the second number equals 6," we can set up a system of equations.
Let's assume the first number is represented by 'x' and the second number is represented by 'y.'
From the given condition, we can translate it into an equation:
2x - y = 6 (equation 1)
We also know that the sum of the two numbers is 15:
x + y = 15 (equation 2)
To solve this system of equations, we can use substitution or elimination.
Let's use the substitution method:
1. Solve equation 2 for x:
x = 15 - y
2. Substitute this expression for x in equation 1:
2(15 - y) - y = 6
Distribute the 2:
30 - 2y - y = 6
Combine like terms:
30 - 3y = 6
Subtract 30 from both sides:
-3y = 6 - 30
-3y = -24
Divide both sides by -3:
y = -24 / -3
y = 8
3. Substitute the value of y in equation 2 to solve for x:
x + 8 = 15
Subtract 8 from both sides:
x = 15 - 8
x = 7
Therefore, the two numbers are 7 and 8, which satisfy both the given sum condition and the equation 2x - y = 6.