/* 
   This script solves a system of two linear equations in 
   Standard Form and displays the steps for the 
   Substitution Method and the Linear Combination Method.

   Copyright (C) 2008 by Allen W. Murphy
   GPL v2 (See below.)
*/

/* ******************************************************************** */
function solution(A, B, C, D, E, F) {
    /* Returns the solution to a linear system
       with two equations and two variables. */
       
    var x1 = (B*F-E*C)/(B*D-E*A);
    var y1 = (E*C*A-B*F*A)/(B*B*D-E*A*B) + C/B;
   
    var point = {x: x1, y: y1};
   
    return point;
}	


/* ******************************************************************** */
function lcm(A, D) {
	
	var minimum = Math.min(Math.abs(A), Math.abs(D));
	
	for (var i=minimum; i<=Math.abs(A)*Math.abs(D); i = i + minimum) {
		if (i % Math.abs(A) == 0 && i % Math.abs(D) == 0) {
			return i;
		}
	}
	
	return i;
}

/* ******************************************************************** */
function linearCombination(output, A, B, C, D, E, F, L) {

	var i = 1; //set the sign of the factor
	
	if (A*(L/A) == D*(L/D)) {
		i = -1;
	}
		
	/* Steps */
	output = output + '<span class="boldblue">Line up terms and get ' + 
		'opposites to eliminate x terms.</span><br />';
	output = output + '<span class="step_gray">(Multiply Equation #1 by ' +
		L/A + " and " + "Equation #2 by " + 1*i*L/D + ".)</span><br />";

	output = output + "(" + A + "x + " + B + "y = " + C + 
		")(" + L/A + ")<br />";
	output = output + "(" + D + "x + " + E + "y = " + F + 
		")(" + (1*i*L/D) + ")<br />";

	output = output + '<span class="step_gray">(The system now looks like ' +
		"this.)</span><br />";
	output = output + L + "x + " + (B*L/A) + "y = " + (C*L/A) + 
		"<br />";
	output = output + -1*L + "x + " + (1*i*E*L/D) + "y = " + 
		(1*i*F*L/D) + "<br />";
		
	output = output + '<br /><span class="boldblue">Add columns down.' +
		"</span><br />";
	output = output + (B*L/A + 1*i*E*L/D) + "y = " + 
		((C*L/A) + (1*i*F*L/D)) + "<br />";

	output = output + '<span class="step_gray">(Divide by ' +
		(B*L/A + 1*i*E*L/D) +".)</span><br />";

	var point = solution(A, B, C, D, E, F);
	output = output + '<span class="boldred">y = ' + point.y + '</span><br />';

	output = output + '<br /><span class="boldblue">Substitute the ' + 
		'y value back into Equation #1:</span><br />';
	output = output +  A + "x + " + B + "(" + point.y + ") = " + C + 
		"<br />";
	output = output + '<span class="step_gray">(Multiply.' + 
		')</span><br />';
	output = output +  A + "x + " + B*point.y + " = " + C + 
		"<br />";
	output = output + '<span class="step_gray">(Subtract ' + B*point.y +
		' from both sides.)</span><br />';
	output = output +  A + "x = " + (1*C + (-1*B*point.y)) + "<br />";
	output = output + '<span class="step_gray">(Divide both sides by ' +
		A + '.)</span><br />';
	output = output +  '<span class="boldred">x = ' + point.x + 
		"</span><br />";

	return output;
}

/* ******************************************************************** */
function solveForY(output, A, B, C) {
	/* Display steps for solving equation 1 for y */
	
	output = output + '<span class="boldblue">Solve Equation 1 for y:</span><br />';
	output = output + A + "x + " + B + "y = " + C + "<br />";
	output = output + '<span class="step_gray">(Subtract ' + A + 
		'x from both sides.)</span><br />';
	output = output + B + "y = " + C + " - (" + A + "x)<br />";
	output = output + '<span class="step_gray">(Divide by ' + B + 
		'.)</span><br />';
	output = output + "y = " + (-A/B) + "x + (" + (C/B) + ")<br />";

	return output;
}

/* ******************************************************************** */
function substituteForY(output, A, B, C, D, E, F){

	output = output + '<br /><span class="boldblue">Substitute for y in ' + 
		'Equation 2:</span><br />';
	output = output + D + "x + " + E + "y = " + F + "<br />";
	output = output + '<span class="step_gray">(Substitute expression' + 
		' for y.)</span><br />';

	output = output + D + "x + " + E + "(" + (-A/B) + 
		"x + (" + (C/B) + ")" +") = " + F + "<br />";
	output = output + '<span class="step_gray">(Distribute ' + E +
		'.)</span><br />';
	output = output + D + "x + " + (-E*A/B) + "x + (" + 
		(E*C/B) + ") = " + F + "<br />";
	output = output + '<span class="step_gray">(Combine like terms.)' + 
		'</span><br />';
		
	var temp = 1*D + (-E*A/B);
	output = output + temp + "x + (" + (E*C/B) + ") = " + F + "<br />";
	output = output + '<span class="step_gray">(Subtract ' + (E*C/B) + 
		' from both sides.)</span><br />';

	output = output + temp + "x = " + (1*F-(E*C/B)) + "<br />";
	output = output + '<span class="step_gray">(Divide by ' + temp + 
		'.)</span><br />';

	var point = solution(A, B, C, D, E, F);
	output = output + '<span class="boldred">x = ' + point.x + '</span><br />';
	
	return output;
}

/* ******************************************************************** */
function substituteForX(output, A, B, C, D, E, F) {

	output = output + '<br /><span class="boldblue">Substitute the ' + 
		'x value back in:</span><br />';
	
	var point = solution(A, B, C, D, E, F);

	output = output + "y = " + (-A/B) + "x + (" + (C/B) + ")<br />";
	output = output + '<span class="step_gray">(Substitute value' + 
		' for x.)</span><br />';

	output = output + "y = " + (-A/B) + "(" + point.x + ") + (" + 
		(C/B) + ")<br />";
	output = output + '<span class="step_gray">(Multiply.' + 
		')</span><br />';

	output = output + "y = " + (-A/B)*point.x + " + (" + (C/B) + ")<br />";
	
	output = output + '<span class="step_gray">(Add.' + 
		')</span><br />';

	output = output + '<span class="boldred">y = ' + point.y + '</span><br />';
	
	return output;
}

/* ******************************************************************** */
function showSteps(output, A, B, C, D, E, F) {

	/* Substitution Method */
	output = output +"<b><u>Substitution Method</u></b><br />";
	output = solveForY(output, A, B, C);
	output = substituteForY(output, A, B, C, D, E, F);
	output = substituteForX(output, A, B, C, D, E, F);
	
	/* Linear Combination Method */
	output = output +"<br /><br /><b><u>Linear " + 
		"Combination Method</u></b><br />";
	output = linearCombination(output, A, B, C, D, E, F, lcm(A, D));
	
	document.getElementById("steps").innerHTML = output;
}

/* ******************************************************************** */
function solveClicked() {
	/* Called when the "Solve" button is clicked. */
	
	var sol;
	var output = "";
	
	var A = document.systemform.A.value;
	var B = document.systemform.B.value;
	var C = document.systemform.C.value;
	var D = document.systemform.D.value;
	var E = document.systemform.E.value;
	var F = document.systemform.F.value;
	
	if (B*D != E*A && B*B*D != E*A*B && B != 0) {
		
		sol = solution(A, B, C, D, E, F);
		
		if (isNaN(sol.x) || isNaN(sol.y)) {
			document.getElementById("result").innerHTML = "Coefficient Error!";
		}
		else {
			document.getElementById("result").innerHTML = "(" + 
				Math.round(sol.x * 100)/100 + ", " + 
				Math.round(sol.y * 100)/100 + ")";
		}
		
		showSteps(output, A, B, C, D, E, F);
	}
	else {
		document.getElementById("result").innerHTML = "No Solution";
	}
	
}
/*
 This script is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2 of the License, or
 (at your option) any later version.

 This script is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 GNU General Public License for more details.

 For a copy of the GNU General Public License write to the Free Software
 Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
*/