Answer:
Let's call the first number x and the second number y. We are given two equations based on the problem:
When you double the first and triple the second, their sum is 1:
2x + 3y = 1
When you triple the first and multiply the second by 5, the sum is 2:
3x + 5y = 2
We now have a system of two equations with two variables. We can solve this system using the method of substitution or elimination. Let's use the elimination method.
Multiply equation 1 by 3 and equation 2 by 2 to make the coefficients of x in both equations equal:
6x + 9y = 3
6x + 10y = 4
Now, subtract equation 1 from equation 2 to eliminate x:
(6x + 10y) - (6x + 9y) = 4 - 3
6x - 6x + 10y - 9y = 1
y = 1
Now that we have found the value of y, we can substitute it back into equation 1 to find x:
2x + 3(1) = 1
2x + 3 = 1
Subtract 3 from both sides:
2x = 1 - 3
2x = -2
Now, divide by 2:
x = -2 / 2
x = -1
So, the two numbers are x = -1 and y = 1.
Explanation:
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