Solution 2.2:6a
From Förberedande kurs i matematik 1
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| + | 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 | ||
| + | <math>\left( x \right.,\left. y \right)</math>, then | ||
| + | |||
| + | <math>y=3x+5</math> | ||
| + | |||
| + | and | ||
| + | |||
| + | <math>y=0</math> | ||
| + | ( | ||
| + | <math>x</math> | ||
| + | -axis) | ||
| + | |||
| + | If we substitute | ||
| + | <math>y=0</math> | ||
| + | into the first equation, we obtain | ||
| + | |||
| + | |||
| + | <math>0=3x+5</math> | ||
| + | i.e. | ||
| + | <math>x=-\frac{5}{3}</math> | ||
| + | |||
| + | |||
| + | The point of intersection is | ||
| + | <math>\left( -\frac{5}{3} \right.,\left. 0 \right)</math>. | ||
| + | |||
| + | |||
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Revision as of 10:16, 18 September 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 \displaystyle \left( x \right.,\left. y \right), then
\displaystyle y=3x+5
and
\displaystyle y=0 ( \displaystyle x -axis)
If we substitute \displaystyle y=0 into the first equation, we obtain
\displaystyle 0=3x+5
i.e.
\displaystyle x=-\frac{5}{3}
The point of intersection is
\displaystyle \left( -\frac{5}{3} \right.,\left. 0 \right).
