Write an efficient, not brute force, program that solves the following problem: suppose we have two unknown quantities x and y. If three time x plus two times y is twenty, and 2 times x plus three time y is ten, what are x and y?
Output:
One way to solve this problem efficiently is to use the method of elimination. We can set up a system of equations as follows:
3x + 2y = 20
2x + 3y = 10
We can then multiply the first equation by 2 and the second equation by 3, to get:
6x + 4y = 40
6x + 9y = 30
We can then subtract the second equation from the first equation, to get:
-5y = 10
y = -2
We can then substitute this value of y into one of the original equations (for example, the first one), to get:
3x + 2(-2) = 20
3x - 4 = 20
3x = 24
x = 8
Therefore, the values of x and y are x = 8 and y = -2.
