Matematyka
Rozwiązanie zadanego układu równań metodą podstawiania:
$\begin{cases}5x-4=3y
\\ 2y+1=3x
\end{cases}$
$-3y+5x=42y-3x=-1
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$varc=document.getElementById("myCanvas");
$
$varctx=c.getContext("2d");
$
$ctx.font="18pxArial";
$
$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.strokeText("y",5,24);ctx.font="12pxArial";
$
$ctx.moveTo(35,24);ctx.lineTo(370,24);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("14",5,48);ctx.moveTo(35,48);ctx.lineTo(370,48);ctx.stroke();
$
$ctx.strokeText("13",5,72);ctx.moveTo(35,72);ctx.lineTo(370,72);ctx.stroke();
$
$ctx.strokeText("12",5,96);ctx.moveTo(35,96);ctx.lineTo(370,96);ctx.stroke();
$
$ctx.strokeText("11",5,120);ctx.moveTo(35,120);ctx.lineTo(370,120);ctx.stroke();
$
$ctx.strokeText("10",5,144);ctx.moveTo(35,144);ctx.lineTo(370,144);ctx.stroke();
$
$ctx.strokeText("9",5,168);ctx.moveTo(35,168);ctx.lineTo(370,168);ctx.stroke();
$
$ctx.strokeText("8",5,192);ctx.moveTo(35,192);ctx.lineTo(370,192);ctx.stroke();
$
$ctx.strokeText("7",5,216);ctx.moveTo(35,216);ctx.lineTo(370,216);ctx.stroke();
$
$ctx.strokeText("6",5,240);ctx.moveTo(35,240);ctx.lineTo(370,240);ctx.stroke();
$
$ctx.strokeText("5",5,264);ctx.moveTo(35,264);ctx.lineTo(370,264);ctx.stroke();
$
$ctx.strokeText("4",5,288);ctx.moveTo(35,288);ctx.lineTo(370,288);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-4",27,310);ctx.moveTo(35,0);ctx.lineTo(35,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-3",51,310);ctx.moveTo(59,0);ctx.lineTo(59,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-2",75,310);ctx.moveTo(83,0);ctx.lineTo(83,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-1",99,310);ctx.moveTo(107,0);ctx.lineTo(107,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("0",123,310);ctx.moveTo(131,0);ctx.lineTo(131,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("1",147,310);ctx.moveTo(155,0);ctx.lineTo(155,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("2",171,310);ctx.moveTo(179,0);ctx.lineTo(179,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("3",195,310);ctx.moveTo(203,0);ctx.lineTo(203,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("4",219,310);ctx.moveTo(227,0);ctx.lineTo(227,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("5",243,310);ctx.moveTo(251,0);ctx.lineTo(251,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("6",267,310);ctx.moveTo(275,0);ctx.lineTo(275,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("7",291,310);ctx.moveTo(299,0);ctx.lineTo(299,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("8",315,310);ctx.moveTo(323,0);ctx.lineTo(323,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("9",339,310);ctx.moveTo(347,0);ctx.lineTo(347,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.beginPath();ctx.moveTo(368,16);ctx.lineTo(206,288);ctx.lineWidth=3;ctx.strokeStyle="#ff3399";ctx.stroke();
$
$ctx.beginPath();ctx.moveTo(368,36);ctx.lineTo(201,288);ctx.lineWidth=3;ctx.strokeStyle="#006633";ctx.stroke();
$
i: Ostateczne rozwiązanie to:
2y = 3x - 1
y = 3x/2 - 1/2
5x - 3•(3x/2-1/2) = 4
x/2 = 5/2
x = 5
x = 5
x = 5
y = 3x/2-1/2 y = (3/2)(5)-1/2 = 7
{x,y} = {5,7}