{% extends arithmetic_template %}
{% block maincode %}
<script language=Javascript1.2><!--
var x1 = get_random(); //the equation can be factored as (x+x1)(x+x2) so he roots are -x1 and -x2
var x2 = get_random();

var multfactor = Math.max(Math.min(get_random(), get_random()),Math.min(get_random(), get_random()));//like to keep this number relatively low so that the graph can be presented well

var A = multfactor;
var B = A*(x1+x2);
var C = A*x1*x2;


var A1 = get_random();
var A2 = get_random();
var B1 = get_random();
var B2 = get_random();
var C1 = get_random();
var C2 = get_random();


while ((B1*A2)==(A1*B2))
{
	var A1 = get_random();
}

var a_lcm = getLCM(Math.abs(A1), Math.abs(A2)); //The least common multiple of the x coefficients
var mult_1 = a_lcm/A1; //What to multiply the top equation by
var mult_2 = a_lcm/A2 * (-1); //What to multiply the bottom equation by..always ends up negative

//get_equation_html('`x='+format_fraction(C1*(B1*mult_1+B2*mult_2)-B1*(C1*mult_1+C2*mult_2),A1*(B1*mult_1+B2*mult_2))+'`'+' , '+get_equation_string(0,1, format_fraction(C1*mult_1+C2*mult_2,B1*mult_1+B2*mult_2) ))	
		
var x_int = (C1*(B1*mult_1+B2*mult_2)-B1*(C1*mult_1+C2*mult_2))/(A1*(B1*mult_1+B2*mult_2));
var y_int = (C1*mult_1+C2*mult_2)/(B1*mult_1+B2*mult_2);

var x_margin=Math.max(Math.abs(x_int), 2);
var x_max = x_int+x_margin;
var x_min = x_int-x_margin;

var y_margin=Math.max(Math.abs(y_int), 2);
var y_max = y_int+y_margin;
var y_min = y_int-y_margin;

function graph_update() {
	initPicture(x_min,x_max, y_min, y_max);
	axes();
	stroke="blue";
	plot("draw_top(x)");
	stroke="green";
	plot("draw_bottom(x)");
	
}

function draw_line(x) {
	return ( A*x*x+B*x+C);
}

function draw_top(x) {
	return ( -1*x*A1/B1+C1/B1);
}

function draw_bottom(x) {
	return ( -1*x*A2/B2 + C2/B2);
}

function write_hint(hint, step)
{
	document.write('<div id=\"step'+step+'\" style=\"position:relative; visibility:hidden;\"><font face=\"arial\" size=3>'+hint+'</font></div>');
}

function get_equation_html(equation)
{
	return ("<center><h3>"+equation+"</h3></center>");
}


function get_equation_string(a_co, b_co, c_co)
{
	if (a_co==0)
		return ('`'+format_first_coefficient(b_co)+'y='+c_co+'`');
	else if (b_co==0)
		return ('`'+format_first_coefficient(a_co)+'x='+c_co+'`');
	else
		return ('`'+format_first_coefficient(a_co)+'x'+format_coefficient(b_co)+'y='+c_co+'`');
}


function write_system(a1_co, b1_co, c1_co, a2_co, b2_co, c2_co)
{
	 return equation_string('`'+get_equation_string(a1_co, b1_co, c1_co)+"<br>"+get_equation_string(a2_co, b2_co, c2_co)+'`');
}

function get_intersection_html(a1_co, b1_co, c1_co, a2_co, b2_co, c2_co)
{

	var intersection = get_intersection(a1_co, b1_co, c1_co, a2_co, b2_co, c2_co);
	return '`x='+format_fraction(intersection[0],intersection[1])+'`'+' , '+get_equation_string(0,1, format_fraction(intersection[2],intersection[3]) );			
}

function get_intersection(a1_co, b1_co, c1_co, a2_co, b2_co, c2_co)
{
	var a_lcm = getLCM(Math.abs(a1_co), Math.abs(a2_co)); //The least common multiple of the x coefficients
	var mult_1 = a_lcm/a1_co; //What to multiply the top equation by
	var mult_2 = a_lcm/a2_co * (-1); //What to multiply the bottom equation by..always ends up negative
	var x_num = (c1_co*(b1_co*mult_1+b2_co*mult_2)-b1_co*(c1_co*mult_1+c2_co*mult_2));
	var x_den = (a1_co*(b1_co*mult_1+b2_co*mult_2));
	var y_num = (c1_co*mult_1+c2_co*mult_2)
	var y_den = (b1_co*mult_1+b2_co*mult_2);

	return [x_num, x_den, y_num, y_den];			
}


//-->
</script>
{% endblock maincode %}

{% block maincell %}
<script language=Javascript1.2><!--
write_text("Solve for `x` and `y`:");

document.write(write_system(A1, B1, C1, A2, B2, C2));
//write out the hints

write_step('You want both `x` coefficients to be the least common multiple of `'+A1+'` and `'+A2+
	   '`.  So you can muliply the top equation by `'+mult_1+'` and the bottom equation by `'+mult_2+'` to get:'+
 	   write_system(A1*mult_1, B1*mult_1, C1*mult_1, A2*mult_2, B2*mult_2, C2*mult_2));

write_step('Adding the top and bottom equations gives you:'+equation_string('`'+get_equation_string(0,B1*mult_1+B2*mult_2, C1*mult_1+C2*mult_2 )+'`'));

if ((B1*mult_1+B2*mult_2)!==1)
	write_step('Dividing both sides by `'+(B1*mult_1+B2*mult_2)+'` gives:'+
			equation_string('`'+get_equation_string(0,1, format_fraction(C1*mult_1+C2*mult_2,B1*mult_1+B2*mult_2) )+'`'));
var final_step ="";

if (A1!=1)
	final_step=equation_string('x='+format_fraction(C1*(B1*mult_1+B2*mult_2)-B1*(C1*mult_1+C2*mult_2),A1*(B1*mult_1+B2*mult_2)));

write_step('Now you can substitute '+
	get_equation_string(0,1, format_fraction(C1*mult_1+C2*mult_2,B1*mult_1+B2*mult_2) )+
	' back into the top equation to get:'+
	equation_string(format_first_coefficient(A1)+'x'+format_coefficient(B1)+'*('+format_fraction(C1*mult_1+C2*mult_2,B1*mult_1+B2*mult_2)+')='+C1)+
	equation_string(format_first_coefficient(A1)+'x'+format_fraction_with_sign(B1*(C1*mult_1+C2*mult_2),B1*mult_1+B2*mult_2)+'='+C1)+
	equation_string(format_first_coefficient(A1)+'x='+format_fraction(C1*(B1*mult_1+B2*mult_2)-B1*(C1*mult_1+C2*mult_2),B1*mult_1+B2*mult_2))+
	final_step+
	equation_string('x='+format_fraction(C1*(B1*mult_1+B2*mult_2)-B1*(C1*mult_1+C2*mult_2),A1*(B1*mult_1+B2*mult_2))+' , '+
			'y='+format_fraction(C1*mult_1+C2*mult_2,B1*mult_1+B2*mult_2)));

var intersection = get_intersection(A1, B1, C1, A2, B2, C2);
var correct_answer = '`x='+format_fraction(intersection[0],intersection[1])+'`';
var correct_answer2 = '`y='+format_fraction(intersection[2],intersection[3])+'`';


function push_fractions_other_than(num, den, varName, results, count) {
	while (results.length < count) {
		var bad_num = get_random();
		var bad_den = get_random();
		if (num*bad_den==den*bad_num || bad_den==0) continue;
		var result = varName + '=' + format_fraction(bad_num, bad_den);
		if ($.inArray(result, results) != -1) continue;
		results.push(result);
	}
}

//Fill in the choices
push_fractions_other_than(intersection[0], intersection[1], "x", Exercise.possibleAnswers, 5);
push_fractions_other_than(intersection[2], intersection[3], "y", Exercise.possibleAnswers2, 5);

//-->
</script>

{% endblock maincell %}
{% block answerarea %}

<span class="info-box-header">Answer</span>
<table border="0" width="200">
<script language=Javascript1.2><!--
	// highly modified multiple-choice code
	// - 2 sets of choices (x and y each have 5)

	//randomly determine which choice will be the correct choice, the math is funky to ensure an equal probability of being any number from 0-4 inclusive
	
    function check_both_answers()
    {
    	if (Exercise.selectedchoice === undefined || Exercise.selectedchoice2 === undefined) 
    	{
    			window.alert("Please choose both answers.");
    			return;
    	}

    	var isCorrect = (Exercise.selectedchoice==Exercise.correctchoice  && Exercise.selectedchoice2==Exercise.correctchoice2);
    	handleCorrectness(isCorrect);
    }
    
    function select_choice(choice)
    {
    	Exercise.selectedchoice = choice;
    }

    function select_choice2(choice)
    {
    	Exercise.selectedchoice2 = choice;
    }
        
	Exercise.correctchoice = Math.round(KhanAcademy.random()*4.98-.49);
	Exercise.correctchoice2 = Math.round(KhanAcademy.random()*4.98-.49); //every variable with a 2 is for the second set of choices

    var answerChoices = new Array(5);
    var answerChoices2 = new Array(5);	
	//Fill in the choices
	//need to fix it so that the other choices can never be the same as the correct choice
    var numChoices=5;
	for (var i=0; i<numChoices; i++)
	{
		if (i==Exercise.correctchoice) 
		{
			answerChoices[i]=correct_answer;
		}
		else
		{
			
			var new_index = Math.round(KhanAcademy.random()*(Exercise.getNumPossibleAnswers() -.02)-.49); //where to pick the new wrong choice
			var new_wrong_choice = Exercise.possibleAnswers.splice(new_index, 1)[0]
			answerChoices[i]='`'+new_wrong_choice+'`';
		}
		if (i==Exercise.correctchoice2) 
		{
			answerChoices2[i]=correct_answer2;
		}
		else
		{
			var new_index = Math.round(KhanAcademy.random()*(Exercise.possibleAnswers2.length-.02)-.49); //where to pick the new wrong choice
			var new_wrong_choice = Exercise.possibleAnswers2.splice(new_index, 1)[0]
			answerChoices2[i]='`'+new_wrong_choice+'`';
		}

		document.write('<tr><td><p style="white-space:nowrap;margin:5px 0"><label for="answerChoiceA'+i+'"><input type="radio" id="answerChoiceA'+i+'" name="selectAnswer" class="select-choice" tabindex="'+(i+1)+'" data-choice="'+i+'">&nbsp;'+answerChoices[i]+'</input></label></p></td>'
		              +'<td><p style="white-space:nowrap;margin:5px 0"><label for="answerChoiceB'+i+'"><input type="radio" id="answerChoiceB'+i+'" name="selectAnswer2" class="select-choice2" tabindex="'+(i+1+numChoices)+'" data-choice="'+i+'">&nbsp;'+answerChoices2[i]+'</input></label></p></td></tr>');
	}

    var $choices = $('.select-choice,.select-choice2');
    $choices.click(function(e) {
        if ($(this).hasClass('select-choice'))
            select_choice(this.getAttribute('data-choice'));
        else
            select_choice2(this.getAttribute('data-choice'));
        
        if (this != document.activeElement)
            $(this).focus();
    });

    $choices.focus(function(e) {
        $(this).click();
    });

    $choices.keypress(function(e) {
        if (e.which == '13') {
            check_answer_block();
            return false;
        }
    });

//-->
</script>
</table>
{% endblock answerarea %}
{% block checkanswer %}check_both_answers(){% endblock checkanswer%}
{% block hintfunction %}give_next_step(){% endblock hintfunction %}