Matematyka
Rozwiązanie zadanego układu równań metodą podstawiania:
$\begin{cases} x+\frac{y}{2}=3
\\ 2x-\frac{y}{3}=5
\end{cases}$
$y+2x=6y+6x=15
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$varc=document.getElementById("myCanvas");
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$varctx=c.getContext("2d");
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$ctx.font="18pxArial";
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$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.strokeText("y",5,24);ctx.font="12pxArial";
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$ctx.moveTo(35,24);ctx.lineTo(300,24);ctx.stroke();
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$ctx.strokeStyle="#202020";ctx.strokeText("4",5,48);ctx.moveTo(35,48);ctx.lineTo(300,48);ctx.stroke();
$
$ctx.strokeText("3",5,72);ctx.moveTo(35,72);ctx.lineTo(300,72);ctx.stroke();
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$ctx.strokeText("2",5,96);ctx.moveTo(35,96);ctx.lineTo(300,96);ctx.stroke();
$
$ctx.strokeText("1",5,120);ctx.moveTo(35,120);ctx.lineTo(300,120);ctx.stroke();
$
$ctx.strokeStyle="#202020";ctx.strokeText("0",5,144);ctx.moveTo(35,144);ctx.lineTo(300,144);ctx.stroke();
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$ctx.strokeStyle="#202020";ctx.strokeText("-1",5,168);ctx.moveTo(35,168);ctx.lineTo(300,168);ctx.stroke();
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$ctx.strokeText("-2",5,192);ctx.moveTo(35,192);ctx.lineTo(300,192);ctx.stroke();
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$ctx.strokeText("-3",5,216);ctx.moveTo(35,216);ctx.lineTo(300,216);ctx.stroke();
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$ctx.strokeText("-4",5,240);ctx.moveTo(35,240);ctx.lineTo(300,240);ctx.stroke();
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$ctx.strokeText("-5",5,264);ctx.moveTo(35,264);ctx.lineTo(300,264);ctx.stroke();
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$ctx.strokeText("-6",5,288);ctx.moveTo(35,288);ctx.lineTo(300,288);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();
$
$ctx.strokeStyle="#202020";ctx.strokeText("1",147,310);ctx.moveTo(155,0);ctx.lineTo(155,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
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$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();
$
$ctx.strokeStyle="#202020";ctx.strokeText("5",243,310);ctx.moveTo(251,0);ctx.lineTo(251,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
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$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.font="18pxArial";
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$ctx.strokeText("x",267,310);ctx.font="11pxArial";
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$ctx.moveTo(275,0);ctx.lineTo(275,290);ctx.strokeStyle='#eee9e9';ctx.stroke();
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$ctx.beginPath();ctx.moveTo(130,0);ctx.lineTo(274,288);ctx.lineWidth=3;ctx.strokeStyle="#ff3399";ctx.stroke();
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$ctx.beginPath();ctx.moveTo(214,0);ctx.lineTo(166,288);ctx.lineWidth=3;ctx.strokeStyle="#006633";ctx.stroke();
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i: Ostateczne rozwiązanie to:
y = -2x + 6
6x - (-2x+6) = 15
8x = 21
8x = 21
x = 21/8
x = 21/8
y = -2x+6 y = -2(21/8)+6 = 3/4
{x,y} = {21/8,3/4}