Rudeš
Sustavi linearnih jednadžbi
<h4>Zadaci - Linearne jednadžbe s dvije nepoznanice</h4>
<p>(a) Riješite sustav linearnih jednadžbi:
\[
§§V1(-10,10,1)§§x + §§V2(-5,5,1)§§y = §§V3(-15,15,1)§§ \\
§§V4(-10,10,1)§§x - y = §§V5(-10,10,1)§§
\]</p>
<svg width="400" height="400">
<!-- Koordinatni sustav -->
<line x1="200" y1="0" x2="200" y2="400" stroke="black" stroke-width="2" />
<line x1="0" y1="200" x2="400" y2="200" stroke="black" stroke-width="2" />
<!-- Mreža točkica -->
<g stroke="lightgray" stroke-width="1">
<!-- Vertikalne linije -->
<line x1="0" y1="0" x2="0" y2="400" stroke-dasharray="2" />
<line x1="50" y1="0" x2="50" y2="400" stroke-dasharray="2" />
<line x1="100" y1="0" x2="100" y2="400" stroke-dasharray="2" />
<line x1="150" y1="0" x2="150" y2="400" stroke-dasharray="2" />
<line x1="250" y1="0" x2="250" y2="400" stroke-dasharray="2" />
<line x1="300" y1="0" x2="300" y2="400" stroke-dasharray="2" />
<line x1="350" y1="0" x2="350" y2="400" stroke-dasharray="2" />
<line x1="400" y1="0" x2="400" y2="400" stroke-dasharray="2" />
<!-- Horizontalne linije -->
<line x1="0" y1="0" x2="400" y2="0" stroke-dasharray="2" />
<line x1="0" y1="50" x2="400" y2="50" stroke-dasharray="2" />
<line x1="0" y1="100" x2="400" y2="100" stroke-dasharray="2" />
<line x1="0" y1="150" x2="400" y2="150" stroke-dasharray="2" />
<line x1="0" y1="250" x2="400" y2="250" stroke-dasharray="2" />
<line x1="0" y1="300" x2="400" y2="300" stroke-dasharray="2" />
<line x1="0" y1="350" x2="400" y2="350" stroke-dasharray="2" />
<line x1="0" y1="400" x2="400" y2="400" stroke-dasharray="2" />
</g>
<!-- Označavanje x-osi -->
<text x="390" y="220" font-family="Arial" font-size="12" fill="black">x</text>
<!-- Označavanje y-osi -->
<text x="210" y="10" font-family="Arial" font-size="12" fill="black">y</text>
<!-- Označavanje vrijednosti varijabli -->
<text x="50" y="220" font-family="Arial" font-size="12" fill="black">§§V1(-10,10,1)§§</text>
<text x="220" y="390" font-family="Arial" font-size="12" fill="black">§§V2(-10,10,1)§§</text>
<text x="190" y="50" font-family="Arial" font-size="12" fill="black">§§V3(-10,10,1)§§</text>
<text x="360" y="220" font-family="Arial" font-size="12" fill="black">§§V4(-10,10,1)§§</text>
<!-- Označavanje točke rješenja -->
<circle cx="200" cy="200" r="5" fill="red" />
</svg>
<p>(b) Riješite sustav linearnih jednadžbi:
\[
2x - y = §§V6(2,8,1)§§ \\
x + §§V7(-5,5,1)§§y = §§V8(-15,15,1)§§
\]</p>
<p>(c) Riješite sustav linearnih jednadžbi:
\[
§§V9(-10,10,1)§§x - 3y = §§V10(-20,20,1)§§ \\
4x + 2y = §§V11(0,10,1)§§
\]</p>
<p>(d) Riješite sustav linearnih jednadžbi:
\[
3x + y = §§V12(5,15,1)§§ \\
x - 2y = §§V13(-5,5,1)§§
\]</p>
<p>(e) Riješite sustav linearnih jednadžbi:
\[
§§V14(-10,10,1)§§x + y = §§V15(-5,5,1)§§ \\
5x - 2y = §§V16(0,10,1)§§
\]</p>
<p>(f) Riješite sustav linearnih jednadžbi:
\[
2x + 3y = §§V17(6,12,1)§§ \\
3x - y = §§V18(5,15,1)§§
\]</p>
<p>(g) Riješite sustav linearnih jednadžbi:
\[
§§V19(-10,10,1)§§x - 2y = §§V20(0,10,1)§§ \\
4x + y = §§V21(8,14,1)§§
\]</p>
<p>(h) Riješite sustav linearnih jednadžbi:
\[
§§V22(-5,5,1)§§x + y = §§V23(3,7,1)§§ \\
2x - 3y = §§V24(-8,8,1)§§
\]</p>
<p>(i) Riješite sustav linearnih jednadžbi:
\[
§§V25(-10,10,1)§§x + §§V26(-5,5,1)§§y = §§V27(6,12,1)§§ \\
4x - y = §§V28(5,15,1)§§
\]</p>
<p>(j) Riješite sustav linearnih jednadžbi:
\[
2x + y = §§V29(1,9,1)§§ \\
§§V30(-10,10,1)§§x - 3y = §§V31(-2,6,1)§§
\]</p>