Systems of Linear Equation in 2 Variable

How many can systems of linear equation have?

1. 1 Solution
   
2. Infinite Solutions
   
3. No Solution
   
   

A) 

If (a1 / a2 != b1 / b2), it involves lines that intersect exactly 1 time.

-- Situation 1

B) 

If (a1 / a2 == b1 / b2 == c1 / c2), it's a same line.

-- Situation 2

C)
If (a1 / a2 == b1 / b2 != c1 / c2), lines are parallel.
-- Situation 3


[Cramer's Rule]

where  is the matrix formed by replacing the ith column of  by the column vector .

 

to solve：http://zerojudge.tw/ShowProblem?problemid=a410
Code:

	/**********************************************************************************/
	/* Problem: a410 "解方程" from TYVJ */
	/* Language: C (552 Bytes) */
	/* Result: AC(0ms, 328KB) judge by this@ZeroJudge */
	/* Author: birdca at 2014-04-24 14:12:05 */
	/**********************************************************************************/
	#include <stdio.h>
	int main()
	{
	int a, b, c, d, e, f;
	while (scanf("%d %d %d %d %d %d", &a, &b, &c, &d, &e, &f) != EOF)
	{
	double tmp = a * e - b * d;
	if (tmp == 0)
	{
	if (c * e == b * f)
	printf("Too many\n");
	else
	printf("No answer\n");
	}
	else
	{
	printf("x=%.2lf\n", (double) (c * e - b * f) / tmp);
	printf("y=%.2lf\n", (double) (a * f - c * d) / tmp);
	}
	}
	return 0;
	}

view raw zerojudge_a410.c hosted with ❤ by GitHub

Ref. http://en.wikipedia.org/wiki/Cramer%27s_rule