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Home » 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.
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.
CBSE | Class 10 | Excercise 3A | Maths | Pair of Linear Equations in Two Variables | RS Aggarwal
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.

Solution:

On a graph paper, draw a horizontal line X^{\prime} O X and a vertical line YOY’ as the x-axis and y-axis, respectively.

Graph of 4 x-5 y+16=0
\begin{array}{l} 4 x-5 y+16=0 \\ \Rightarrow 5 y=(4 x+16) \\ \therefore y=\frac{4 x+16}{5} \ldots \ldots \ldots . \end{array}

Putting x=1, we obtain y=4.
Putting x=-4, we obtain y=0.
Putting x=6, we obtain y=8.

Therefore, we have the following table for the equation 4 x-5 y+16=0.

    \[\begin{tabular}{|c|c|c|c|} \hline$x$ & 1 & $-4$ & 6 \\ \hline$y$ & 4 & 0 & 8 \\ \hline \end{tabular}\]

Now, plot the points A(1,4), B(-4,0) and C(6,8) on the graph paper.
Join A B and A C to get the graph line B C. Extend it on both ways.

So, B C is the graph of 4 x-5 y+16=0
\begin{array}{l} \text { Graph of } 2 x+y-6=0 \\ 2 x+y-6=0 \\ \Rightarrow y=(-2 x+6) \ldots \ldots \ldots . \text { (ii) } \end{array}

Putting x=1, we obtain y=4.
Putting x=3, we obtain y=0.
Putting x=2, we obtain y=2.

So, we have the following table for the equation 2 x+y-6=0.

    \[\begin{tabular}{|l|l|l|l|} \hline$x$ & 1 & 3 & 2 \\ \hline$y$ & 4 & 0 & 2 \\ \hline \end{tabular}\]

Now, plot the points P(3,0) and Q(2,2). The point A(1,4) has already been plotted. Join P Q and Q A to get the graph line P A. Extend it on both ways Then, P A is the graph of the equation 2 x+y-6=0.


The two graph lines intersect at A(1,4).
\therefore The solution of the given system of equations is x=1 and y=4.
As a result, these lines form \triangle B A P with the x-axis, whose vertices are B(-4,0), A(1,4) and P(3,0).

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