Question

Draw a graph of the equation \[5x - y = 5,{\text{ }}3x - y = 3\]. Determine the coordinates of the vertices of the triangle formed by these lines and y axis.

Answer 1

Hint: At first we have to solve the linear equations to get the value of ${\text{x and y}}$
Finally we have to put the values and draw a line on the graph paper.

Complete step-by-step answer:
It is given in the question that
$5x - y = 5...\left( 1 \right)$
$3x - y = 3...\left( 2 \right)$
Now, by solving equation $\left( 1 \right)$ we get
$5x - y = 5$
 $5x - 5 = y$
 $y = 5x - 5...\left( 3 \right)$
 Now let the value of $x = 0$ and put it in the above equation $\left( 3 \right)$ we get
$y = 5\left( 0 \right) - 5 = - 5$
So $(0, - 5)$ is a solution
Again let $x = 1$ and putting it in equation $\left( 3 \right)$ we get
$y = 5\left( 1 \right) - 5 = 0$
Here $(1,0)$is a solution
Now, by solving equation $\left( 2 \right)$ we get-
$3x - y = 3$
$3x - 3 = y$
Again, let the value of $x = 0,$ and putting it in equation $\left( 2 \right)$ we get
$y = 3\left( 0 \right) - 3 = - 3$
So $(0, - 3)$ is a solution
Suppose the value of $x = 1$ and putting it in equation $\left( 2 \right)$ we get
$y = 3\left( 1 \right) - 3 = 3 - 3 = 0$
So $(1,0)$ is a solution
Now after getting the solution of both the equations, we will put the value on the graph paper.
Here is the graphical representation of the solution.

Thus, the required triangle is $\Delta ABC$ where $A(1,0),B(0, - 3),C(0, - 5)$.

Note: It must be kept in mind while making a graph that the linear equations which are given in the question must be solved and the values of the solution will be plotted in the graph to get the resultant.
Coordinates of triangles is one of very important concepts in coordinate geometry because with the coordinates of a triangle the area of any triangle can be easily found out. Formula for finding out the area of the triangle with coordinates is $\dfrac{1}{2}[{x_1}({y_2} - {y_3}) + {x_2}({y_3} - {y_1}) + {x_3}({y_1} - {y_2})]$