Solve the following system of equations graphically: 4x-5y+16=0, 2x+y-6=0. Determine the vertices of the triangle formed by these lines and the x-axis.
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Solution:
On a graph paper, draw a horizontal line and a vertical line YOY’ as the -axis and -axis, respectively.
Graph of
Putting , we obtain .
Putting , we obtain .
Putting , we obtain .
Therefore, we have the following table for the equation .
Now, plot the points and on the graph paper.
Join and to get the graph line . Extend it on both ways.
So, is the graph of
Putting , we obtain .
Putting , we obtain .
Putting , we obtain .
So, we have the following table for the equation .
Now, plot the points and . The point has already been plotted. Join and to get the graph line . Extend it on both ways Then, is the graph of the equation .
The two graph lines intersect at . The solution of the given system of equations is and .
As a result, these lines form with the -axis, whose vertices are and .
![\[\begin{tabular}{|c|c|c|c|} \hline$x$ & 1 & $-4$ & 6 \\ \hline$y$ & 4 & 0 & 8 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-29c411ffad9fa835bf3423f04a274f70_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{tabular}{|l|l|l|l|} \hline$x$ & 1 & 3 & 2 \\ \hline$y$ & 4 & 0 & 2 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-61362ad8c7e2f1cd1cb7cba64f424ddd_l3.png "Rendered by QuickLaTeX.com")
