Problem A
Equations
Given $2$ linear equations on the variables $x$ and $y$, solve for $x$ and $y$.
Input
The first line of input contains an integer $1 \le N \le 100$, the number of test cases. Each test case consists of two equations, each on a separate line. An empty line separates cases.
An equation consists of at least $2$ and at most $10$ terms separated by addition, subtraction, or equality operators. A term is an integer, or a variable name ($x$ or $y$) optionally preceded by a minus sign or an integer coefficient. There is exactly one equality operator. Constant terms and coefficients are at most $100$ in absolute value. All operators are surrounded by spaces, and there are no spaces within terms.
Output
For each case, print two lines, giving the values of $x$ and $y$ as rationals in simplest terms. If $x$ or $y$ has no unique rational value such that both equations hold, print “don’t know” for its value. Print an empty line between cases.
| Sample Input 1 | Sample Output 1 |
|---|---|
7 2x + 3y = x 5 = x + y + 3 2x + 3y = 0 10x = -15y 2x + 3y = 0 10x = -15y + 1 x = 1 3x = 6y 2x = 3x + -x + y x + y = x + y 2x = -3 -2y = 3 1 = 2 x = 3 |
3 -1 don't know don't know don't know don't know 1 1/2 don't know 0 -3/2 -3/2 don't know don't know |
