Question

Draw the graphs of the equations 5x − y = 5 and 3x − y = 3. Determine the co- ordinates of the vertices of the triangle formed by these lines and the y axis.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of lines are

$\rm :\longmapsto\:5x - y = 5 - - - (1)$

and

$\rm :\longmapsto\:3x - y = 3 - - - (2)$

Now Let sketch the graph of the lines.

Consider Line (1).

$\rm :\longmapsto\:5x - y = 5 - - - (1)$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 - y = 5$

$\rm :\longmapsto\:- y = 5$

$\rm :\longmapsto\:y = - 5$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:5x - 0 = 5$

$\rm :\longmapsto\:5x = 5$

$\rm :\longmapsto\:x = 1$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 5 \\ \\ \sf 1 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 5) & (1 , 0)

➢ See the attachment graph.

Now, Consider Line (2)

$\rm :\longmapsto\:3x - y = 3 - - - (2)$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 - y = 3$

$\rm :\longmapsto\: - y = 3$

$\rm :\longmapsto\: y = - 3$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:3x - 0 = 3$

$\rm :\longmapsto\:3x = 3$

$\rm :\longmapsto\:x = 1$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 3 \\ \\ \sf 1 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 3) & (1 , 0)

➢ See the attachment graph.

Now,

From graph we concluded that triangle ABC is the required triangle formed by lines with y - axis.

Hence, Coordinates of triangle ABC are

Coordinates of A (0, - 3)

Coordinates of B (0, - 5)

Coordinates of C (1, 0)

Answer 2

Solution:-

To draw the graph Take out 2-2 pairs of solution for both equations

equation 1

$\large \mathtt{ 5x - y = 5}$

Put Y=0

$\large \mathtt{ 5x - 0= 5 : \rightarrow \: x = 1 }$

put Y=5

$\large \mathtt{ 5x - 5 = 5 : \rightarrow \: x = 2 }$

from here we get 2 pairs of X and Y for the equation 1

1. (x,y)=(1,0)
2. (x,y)=(2,5)

Similarly find out 2 pairs of X and Y from equation 2

$\large \mathtt{ 3x - y = 3}$

2 pairs can be

1. (x,y)=(1,0)
2. (x,y)=(2,3)

Now plot these values in graph to get graph of equations

Hence the points of triangle are

• (0,-3)
• (1,0)
• (0,-5)

For better understanding go through graph provided in attachment.