The sum of twice a number and another number is 24. The difference of twice the first number and the other number is 12. Which system would model this situation, and what is the solution?
x = 1st number and y = second number
2x + y = 24
2x - y = 12
Can you finish from here? Add the two equations to eliminate y and solve for x.
Then find y.
Be sure to check both x and y in both equations to be sure you are correct.
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To model this situation, we can use a system of equations. Let's call the first number "x" and the other number "y".
According to the problem, the sum of twice a number and another number is 24:
2x + y = 24 -- Equation (1)
The difference of twice the first number and the other number is 12:
2x - y = 12 -- Equation (2)
We have now formed a system of equations. To solve this system, we can use the method of elimination. In this case, we will eliminate the variable "y".
To eliminate "y", we can add Equation (1) and Equation (2):
(2x + y) + (2x - y) = 24 + 12
4x = 36
x = 9
Now, substitute the value of x (9) into either Equation (1) or Equation (2) to solve for y. Let's use Equation (1):
2(9) + y = 24
18 + y = 24
y = 6
Therefore, the solution to this system of equations is x = 9 and y = 6.
2 x + y = 24
y - 2x = 12
4 x = 12
x = 3
y = 24 - 6 = 18
check
6 + 18 = 24 yes
18 - 6 = 12 yes
note you could have written
2 x + y = 24
2 x - y = 12
2 y = 12
y = 6
2x + 6 = 24
x = 9