Matematyka
gdzie jesteś: Start
/ Układy równań
/ Układy równań - metoda podstawiania
/ Rozwiąż układ równań dla x+y=35 i y=2x+5
Rozwiąż układ równań dla x+y=35 i y=2x+5
Rozwiązanie zadanego układu równań metodą podstawiania:
$\begin{cases}x+y=35
\\ y=2x+5
\end{cases}$
$y+x=35y-2x=5
$
$
$
$
$
$varc=document.getElementById("myCanvas");
$
$varctx=c.getContext("2d");
$
$ctx.font="18pxArial";
$
$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.strokeText("y",7,24);ctx.font="12pxArial";
$
$ctx.moveTo(27,24);ctx.lineTo(291,24);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("29",7,48);ctx.moveTo(27,48);ctx.lineTo(291,48);ctx.stroke();
$
$ctx.strokeText("28",7,72);ctx.moveTo(27,72);ctx.lineTo(291,72);ctx.stroke();
$
$ctx.strokeText("27",7,96);ctx.moveTo(27,96);ctx.lineTo(291,96);ctx.stroke();
$
$ctx.strokeText("26",7,120);ctx.moveTo(27,120);ctx.lineTo(291,120);ctx.stroke();
$
$ctx.strokeText("25",7,144);ctx.moveTo(27,144);ctx.lineTo(291,144);ctx.stroke();
$
$ctx.strokeText("24",7,168);ctx.moveTo(27,168);ctx.lineTo(291,168);ctx.stroke();
$
$ctx.strokeText("23",7,192);ctx.moveTo(27,192);ctx.lineTo(291,192);ctx.stroke();
$
$ctx.strokeText("22",7,216);ctx.moveTo(27,216);ctx.lineTo(291,216);ctx.stroke();
$
$ctx.strokeText("21",7,240);ctx.moveTo(27,240);ctx.lineTo(291,240);ctx.stroke();
$
$ctx.strokeText("20",7,264);ctx.moveTo(27,264);ctx.lineTo(291,264);ctx.stroke();
$
$ctx.strokeText("19",7,288);ctx.moveTo(27,288);ctx.lineTo(291,288);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("4",19,310);ctx.moveTo(27,0);ctx.lineTo(27,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("5",43,310);ctx.moveTo(51,0);ctx.lineTo(51,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("6",67,310);ctx.moveTo(75,0);ctx.lineTo(75,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("7",91,310);ctx.moveTo(99,0);ctx.lineTo(99,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("8",115,310);ctx.moveTo(123,0);ctx.lineTo(123,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("9",139,310);ctx.moveTo(147,0);ctx.lineTo(147,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("10",163,310);ctx.moveTo(171,0);ctx.lineTo(171,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("11",187,310);ctx.moveTo(195,0);ctx.lineTo(195,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("12",211,310);ctx.moveTo(219,0);ctx.lineTo(219,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("13",235,310);ctx.moveTo(243,0);ctx.lineTo(243,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.font="18pxArial";
$
$ctx.strokeText("x",259,310);ctx.font="11pxArial";
$
$ctx.moveTo(267,0);ctx.lineTo(267,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.beginPath();ctx.moveTo(289,264);ctx.lineTo(27,0);ctx.lineWidth=3;ctx.strokeStyle="#ff3399";ctx.stroke();
$
$ctx.beginPath();ctx.moveTo(241,0);ctx.lineTo(98,288);ctx.lineWidth=3;ctx.strokeStyle="#006633";ctx.stroke();
$
i: Ostateczne rozwiązanie to:
y = 2x + 5
x + (2x+5) = 35
3x = 30
3x = 30
x = 10
x = 10
y = 2x+5 y = 2(10)+5 = 25
{x,y} = {10,25}
