Lösung 2.2:6a

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If the point of intersection has coordinates (''x'',''y''), then
If the point of intersection has coordinates (''x'',''y''), then
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<math>\left\{\begin{align} y&=3x+5\,,\\ y&=0\,\textrm{.}\qquad\quad\text{(x-axis)}\end{align}\right.</math>}}
<math>\left\{\begin{align} y&=3x+5\,,\\ y&=0\,\textrm{.}\qquad\quad\text{(x-axis)}\end{align}\right.</math>}}
If we substitute <math>y=0</math> into the first equation, we obtain
If we substitute <math>y=0</math> into the first equation, we obtain
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{{Displayed math||<math>0=3x+5,\qquad\text{i.e.}\quad x=-\frac{5}{3}\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>0=3x+5,\qquad\text{i.e.}\quad x=-\frac{5}{3}\,\textrm{.}</math>}}
The point of intersection is (-5/3,0).
The point of intersection is (-5/3,0).

Version vom 08:29, 22. Okt. 2008

According to the definition, the point of intersection between two lines is that point which lies on both lines; it must therefore satisfy the equations of both lines.

If the point of intersection has coordinates (x,y), then

\displaystyle \left\{\begin{align} y&=3x+5\,,\\ y&=0\,\textrm{.}\qquad\quad\text{(x-axis)}\end{align}\right.

If we substitute \displaystyle y=0 into the first equation, we obtain

\displaystyle 0=3x+5,\qquad\text{i.e.}\quad x=-\frac{5}{3}\,\textrm{.}

The point of intersection is (-5/3,0).


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