Question

Solve the following system of equations graphically. Determine the vertices of the triangle formed by the lines and the given axis.

$4x-5y-20=0;3x+5y-15=0,y-axis$

Answer 1

Step 1:Solving and analyzing the first equation to find the values for $xandy$

Consider the first equation given

$4x-5y-20=0.................................\left(1\right)$

Solving the equation

$$\begin{gathered} 4x-5y-20=0 \\ 4x=5y+20 \end{gathered}$$

$x=\frac{5y+20}{4}................................\left(2\right),$Let this be the equation of x in terms of y

Now, Substituting y values as $0,1,2$ in equation (2) ,we get the following x-values.

$x$	$5$	$6.25$	$7.5$
$y$	$0$	$1$	$2$

Step 2:Solving and analyzing the second equation to find the values for $xandy$

Consider the second equation given,

$3x+5y-15=0..............................\left(3\right)$

Solving the equation

$3x=15-5y$

$x=\frac{15-5y}{3}..........................................\left(4\right),$Let this be the equation of x in terms of y.

Now, Substituting y values as $0,1,2$in equation (4),we get

$x$	$5$	$3.3$	$1.6$
$y$	$0$	$1$	$2$

Step 3:Graphical representation.

Plotting the points obtained on the graph, we get the representation of the solution as given below:-

Hence, the vertices of the triangle formed on y-axis are $(0,3),(0,-4),(5,0).$.