<ul class="bullet-list"><li data-list-item-id="item-1780989259307-next8helb"><div class="list-item-paragraph">Solving simultaneous non-linear equations involved \(2\) or more equations that are non linear.</div></li><li data-list-item-id="item-1780989259726-to6o40j3o"><div class="list-item-paragraph">In this unit it will involve quadratic equations of the general form \(y = ax^2 + bx + c\) and a linear equation with a general form of \(y = mx + c\).</div></li><li data-list-item-id="item-1780989260109-ad0i7u7ao"><div class="list-item-paragraph">The solution of the simultaneous equation will be the point(s) of intersection between the line and the curve.</div></li><li data-list-item-id="item-1780989260613-2frbzse8o"><div class="list-item-paragraph">The nature of the point(s) of intersections, can be used to find unknown coefficients in the equation and is summarised in the table below:</div></li></ul>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><p><strong>Nature of points of intersection</strong></p></th><th style="text-align: center; --cell-justify: center"><p><strong>Graphical representation</strong></p></th><th style="text-align: center; --cell-justify: center"><p><strong>Determinant</strong></p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>Line intersects with the curve at \(2\) points</p></td><td style="text-align: center; --cell-justify: center"><div class="graph-block" data-graph-config="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" data-width="150" data-height="100" style="width:150px;height:100px;max-width:100%;display:block;margin:0 auto;"></div></td><td style="text-align: center; --cell-justify: center"><p>\(b^2 - 4ac &gt; 0\)</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>The line intersects is tangent to the curve and intersects at \(1\) point</p></td><td style="text-align: center; --cell-justify: center"><div class="graph-block" data-graph-config="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" data-width="150" data-height="100" style="width:150px;height:100px;max-width:100%;display:block;margin:0 auto;"></div></td><td style="text-align: center; --cell-justify: center"><p>\(b^2 - 4ac = 0\)</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>The line does not intersect the curve</p></td><td style="text-align: center; --cell-justify: center"><div class="graph-block" data-graph-config="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" data-width="150" data-height="100" style="width:150px;height:100px;max-width:100%;display:block;margin:0 auto;"></div></td><td style="text-align: center; --cell-justify: center"><p>\(b^2 - 4ac &lt; 0\)</p></td></tr></tbody></table></div></div>

Solving simultaneous non-linear equations involved \(2\) or more equations that are non linear.

In this unit it will involve quadratic equations of the general form \(y = ax^2 + bx + c\) and a linear equation with a general form of \(y = mx + c\).

The solution of the simultaneous equation will be the point(s) of intersection between the line and the curve.

The nature of the point(s) of intersections, can be used to find unknown coefficients in the equation and is summarised in the table below:

<p><strong>Nature of points of intersection</strong></p>

<p><strong>Graphical representation</strong></p>

<p>Line intersects with the curve at \(2\) points</p>

<p>The line intersects is tangent to the curve and intersects at \(1\) point</p>

Intersection of a Line and Curve

Intersection of a Line and Curve