Kattis

# 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