Question

I have to find out at which points the lines intersectY= .5x+3 & Y= 2x-9

Answer 1

We want to find out at which points the lines

`\begin{gathered} y=0.5x+3\text{ and } \\ y=2x-9 \end{gathered}`

intersect.

To do this, we have to solve the equations simultaneously and look for the values of x and y.

This becomes

`\begin{gathered} y=0.5x+3\ldots\ldots\ldots\text{.}\mathrm{}eq\text{ 1} \\ y=2x-9\ldots\ldots\ldots\ldots\text{.}\mathrm{}eq\text{ 2} \\ \text{subtracting equation 2 from 1, we have } \\ y-y=(0.5x-2x)+(3-(-9) \\ 0=-1.5x+(3+9) \\ 1.5x=(3+9) \\ 1.5x=12 \end{gathered}`

Dividing both sides by 1.5, we get x, this becomes

`\begin{gathered} (1.5x)/(1.5)=(12)/(1.5) \\ x=8 \end{gathered}`

To get y, we substitute the x for 8 into equation 1 or 2. Let us use equation 1, we have