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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>
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