Question

draw the graph of the following equations y-x=1 and x+y=3. shade the region bounded by the two lines and the line y=0​

Answer 1

Step-by-step explanation:

clearly

y-x= 1 is a straight line passing through -1and 1 respectively.

x+y=3 is also a straight line passing through 3 and 3 respectively.

Answer 2

Answer:

Refer to the attachment.

Step-by-step explanation:

We've been given two equations. We'll first find coordinates for 'x' and 'y' for each equation, then plot them on the cartesian plane.

$\sf \underline{Equation \ 1}\\ \\ \\\sf y - x = 1\\ \\\sf y = 1 + x\\ \\ \\\begin{array}{| c | c | c | c |}\cline{1-4} \sf \ x \ & \sf -1 \ & \sf \ 1 \ & \sf \ 2 \ \\\cline{1-4} \sf \ y \ & \sf \ 0 & \sf \ 2 \ & \sf \ 3 \ \\\cline{1-4}\end{array}\\ \\ \\\sf Coordinates: (-1,0), \ (1, 2) \ and \ (2, 3)$

$\sf \underline{Equation \ 2}\\ \\ \\\sf x + y = 3\\ \\\sf y = 3 - x\\ \\ \\\begin{array}{| c | c | c | c |}\cline{1-4} \sf \ x \ & \sf \ 3 \ & \sf \ 1 \ & \sf \ 2 \ \\\cline{1-4} \sf \ y \ & \sf \ 0 \ & \sf \ 2 \ & \sf \ 1 \ \\\cline{1-4}\end{array}\\ \\ \\\sf Coordinates: (3,0), \ (1, 2) \ and \ (2, 1)$

We are asked to shade the area formed by these two lines with the like y = 0, which means we have to shade the area bound by the two lines and x-axis.

(Refer to the attachment)

The orange line represents the equation y - x = 1.

The black line represents the equation x + y = 3.

Things to remember while plotting a graph.

1. Mark the x-axis and the y-axis along with the arrows.

2. Write the equation above the line you've drawn.

3. Shade the area if you're asked to.

4. Mark the coordinates.