Matematyka
Rozwiązanie zadanego układu równań metodą podstawiania:
$\begin{cases}2x-5y-2=0
\\ 3x-6y+1=0
\end{cases}$
$-5y+2x=2-6y+3x=-1
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$varc=document.getElementById("myCanvas");
$
$varctx=c.getContext("2d");
$
$ctx.font="18pxArial";
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$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.strokeText("y",7,24);ctx.font="12pxArial";
$
$ctx.moveTo(27,24);ctx.lineTo(291,24);ctx.stroke();
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$ctx.strokeStyle="#202020";ctx.strokeText("2",7,48);ctx.moveTo(27,48);ctx.lineTo(291,48);ctx.stroke();
$
$ctx.strokeText("1",7,72);ctx.moveTo(27,72);ctx.lineTo(291,72);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("0",7,96);ctx.moveTo(27,96);ctx.lineTo(291,96);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-1",7,120);ctx.moveTo(27,120);ctx.lineTo(291,120);ctx.stroke();
$
$ctx.strokeText("-2",7,144);ctx.moveTo(27,144);ctx.lineTo(291,144);ctx.stroke();
$
$ctx.strokeText("-3",7,168);ctx.moveTo(27,168);ctx.lineTo(291,168);ctx.stroke();
$
$ctx.strokeText("-4",7,192);ctx.moveTo(27,192);ctx.lineTo(291,192);ctx.stroke();
$
$ctx.strokeText("-5",7,216);ctx.moveTo(27,216);ctx.lineTo(291,216);ctx.stroke();
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$ctx.strokeText("-6",7,240);ctx.moveTo(27,240);ctx.lineTo(291,240);ctx.stroke();
$
$ctx.strokeText("-7",7,264);ctx.moveTo(27,264);ctx.lineTo(291,264);ctx.stroke();
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$ctx.strokeText("-8",7,288);ctx.moveTo(27,288);ctx.lineTo(291,288);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-11",19,310);ctx.moveTo(27,0);ctx.lineTo(27,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-10",43,310);ctx.moveTo(51,0);ctx.lineTo(51,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-9",67,310);ctx.moveTo(75,0);ctx.lineTo(75,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-8",91,310);ctx.moveTo(99,0);ctx.lineTo(99,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-7",115,310);ctx.moveTo(123,0);ctx.lineTo(123,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-6",139,310);ctx.moveTo(147,0);ctx.lineTo(147,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-5",163,310);ctx.moveTo(171,0);ctx.lineTo(171,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-4",187,310);ctx.moveTo(195,0);ctx.lineTo(195,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-3",211,310);ctx.moveTo(219,0);ctx.lineTo(219,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("-2",235,310);ctx.moveTo(243,0);ctx.lineTo(243,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.font="18pxArial";
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$ctx.strokeText("x",259,310);ctx.font="11pxArial";
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$ctx.moveTo(267,0);ctx.lineTo(267,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
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$ctx.beginPath();ctx.moveTo(289,105);ctx.lineTo(27,211);ctx.lineWidth=3;ctx.strokeStyle="#ff3399";ctx.stroke();
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$ctx.beginPath();ctx.moveTo(289,92);ctx.lineTo(27,224);ctx.lineWidth=3;ctx.strokeStyle="#006633";ctx.stroke();
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i: Ostateczne rozwiązanie to:
3x = 6y - 1
x = 2y - 1/3
2•(2y-1/3) - 5y = 2
- y = 8/3
- 3y = 8
3y = - 8
y = - 8/3
x = 2y-1/3
y = -8/3 x = 2(-8/3)-1/3 = -17/3
{x,y} = {-17/3,-8/3}