Rozwiąż układ równań dla k+l/2=3 i 2k-1/3l=5

Rozwiązanie zadanego układu równań metodą podstawiania:

$\begin{cases} k+\frac{l}{2}=3 \\  2k-\frac{l}{3}=5 \end{cases}$

$l+2k=6l+6k=15 $
$ $
$ $
$varc=document.getElementById("myCanvas"); $
$varctx=c.getContext("2d"); $
$ctx.font="18pxArial"; $
$ctx.strokeStyle="#202020";ctx.strokeStyle="#b22222";ctx.strokeText("l",7,24);ctx.font="12pxArial"; $
$ctx.moveTo(27,24);ctx.lineTo(291,24);ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("4",7,48);ctx.moveTo(27,48);ctx.lineTo(291,48);ctx.stroke(); $
$ctx.strokeText("3",7,72);ctx.moveTo(27,72);ctx.lineTo(291,72);ctx.stroke(); $
$ctx.strokeText("2",7,96);ctx.moveTo(27,96);ctx.lineTo(291,96);ctx.stroke(); $
$ctx.strokeText("1",7,120);ctx.moveTo(27,120);ctx.lineTo(291,120);ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("0",7,144);ctx.moveTo(27,144);ctx.lineTo(291,144);ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("-1",7,168);ctx.moveTo(27,168);ctx.lineTo(291,168);ctx.stroke(); $
$ctx.strokeText("-2",7,192);ctx.moveTo(27,192);ctx.lineTo(291,192);ctx.stroke(); $
$ctx.strokeText("-3",7,216);ctx.moveTo(27,216);ctx.lineTo(291,216);ctx.stroke(); $
$ctx.strokeText("-4",7,240);ctx.moveTo(27,240);ctx.lineTo(291,240);ctx.stroke(); $
$ctx.strokeText("-5",7,264);ctx.moveTo(27,264);ctx.lineTo(291,264);ctx.stroke(); $
$ctx.strokeText("-6",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("-3",43,310);ctx.moveTo(51,0);ctx.lineTo(51,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("-2",67,310);ctx.moveTo(75,0);ctx.lineTo(75,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("-1",91,310);ctx.moveTo(99,0);ctx.lineTo(99,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("0",115,310);ctx.moveTo(123,0);ctx.lineTo(123,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("1",139,310);ctx.moveTo(147,0);ctx.lineTo(147,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("2",163,310);ctx.moveTo(171,0);ctx.lineTo(171,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("3",187,310);ctx.moveTo(195,0);ctx.lineTo(195,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("4",211,310);ctx.moveTo(219,0);ctx.lineTo(219,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.strokeStyle="#202020";ctx.strokeText("5",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("k",259,310);ctx.font="11pxArial"; $
$ctx.moveTo(267,0);ctx.lineTo(267,290);ctx.strokeStyle='#eee9e9';ctx.stroke(); $
$ctx.beginPath();ctx.moveTo(122,0);ctx.lineTo(265,288);ctx.lineWidth=3;ctx.strokeStyle="#ff3399";ctx.stroke(); $
$ctx.beginPath();ctx.moveTo(205,0);ctx.lineTo(158,288);ctx.lineWidth=3;ctx.strokeStyle="#006633";ctx.stroke(); $

i: Ostateczne rozwiązanie to:

l = -2k + 6

  6k - (-2k+6) = 15
  8k = 21
  8k = 21 

  k = 21/8 
  k = 21/8
  l = -2k+6  l = -2(21/8)+6 = 3/4 
 {k,l} = {21/8,3/4} 



Podziel się rozwiązaniem: