Answer:
Using Geometry to answer the question would be the simplest:
Step-by-step explanation:
Remembering the formula for the area of a triangle which is
. One can then tackle the question by doing the following:
Step 1 Find the y-intercepts
The y-intercepts are found by substituting in
.
Which gives you this when you plug it into both equations:
![-y=1\\y=-1\\y=8](https://tex.z-dn.net/?f=-y%3D1%5C%5Cy%3D-1%5C%5Cy%3D8)
So the y-intercepts for the graphs are
, and
respectively.
Now one has to use elimination to solve the problems by adding up the equations we get:
![x-y=1\\2x+y=8\\3x=9\\x=3](https://tex.z-dn.net/?f=x-y%3D1%5C%5C2x%2By%3D8%5C%5C3x%3D9%5C%5Cx%3D3)
Now to solve for the y component substitute:
![2(3)+y=8\\y=2](https://tex.z-dn.net/?f=2%283%29%2By%3D8%5C%5Cy%3D2)
Therefore, the graphs intersect at the following:
![(3,2)](https://tex.z-dn.net/?f=%283%2C2%29)
Now we have our triangle which is accompanied by the graph.
now to solve it we must figure out how long the base is:
![b=8-(-1)\\b=9](https://tex.z-dn.net/?f=b%3D8-%28-1%29%5C%5Cb%3D9)
The height must also be accounted for which is the following:
![h=3](https://tex.z-dn.net/?f=h%3D3)
Now the formula can be used:
![A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2](https://tex.z-dn.net/?f=A%3D%5Cfrac12bh%3D%5Cfrac12%289%29%283%29%3D%5Cfrac%7B27%7D2%5C%20%5Ctext%7Bunits%7D%5E2)