Question

Draw the graph of the following equations. Also Determine the Coordinates of the vertices of the triangle formed by these lines and the x-axis.

$4x-5y+16=0;2x+y-6=0$

Answer 1

Step 1:Consider the first equation,

$$\begin{gathered} 4x-5y-16=0 \\ \Rightarrow x=\frac{5y-16}{4}------\left(1\right) \end{gathered}$$

Substituting 0,1,2 as values of Y in equation (1),we get x values as follows,

x	-4	-2.7	-1.5
y	0	1	2

Step 2: Consider the second equation

$$\begin{gathered} 2x+y-6=0 \\ \Rightarrow x=\frac{6-y}{2}------\left(2\right) \end{gathered}$$

Substituting 0,1,2 as values of y in equation (2), we get x values as follows,

x	3	2.5	2
y	0	1	2

Step 3: Plotting the values obtained from both first and second equations:

Hence, The coordinates of a triangle formed by the lines and the x-axis are (-4,0) (3,0) (1,4).