Draw the graph of the following equations : $x + y = 5$ , $x - y = 5$ , and (i) find the solution of the equations from the graph. (ii) shade the triangular region formed by the lines and the y-axis.

Answer: (i) The solution to the equations is $(5, 0)$ . (ii) The triangular region formed by the lines and the $y$ -axis has vertices $(0, 5)$ , $(0, -5)$ , and $(5, 0)$ .

Step-by-step solution

Step 1: Find points for the first equation

To graph the line $x + y = 5$ , we find two points that satisfy the equation. If $x = 0$ , then $y = 5$ , giving the point $(0, 5)$ . If $y = 0$ , then $x = 5$ , giving the point $(5, 0)$ .

Step 2: Find points for the second equation

Similarly, for the line $x - y = 5$ , we find two points. If $x = 0$ , then $-y = 5$ , so $y = -5$ , giving the point $(0, -5)$ . If $y = 0$ , then $x = 5$ , giving the point $(5, 0)$ .

Step 3: Plot the lines and find the intersection

We plot the points and draw the lines. The intersection point of the two lines is the solution to the system of equations. From the graph, both lines pass through the point $(5, 0)$ .

Step 4: Identify and shade the triangular region

The two lines intersect at $(5, 0)$ . The first line $x + y = 5$ intersects the $y$ -axis at $(0, 5)$ . The second line $x - y = 5$ intersects the $y$ -axis at $(0, -5)$ . These three points form a triangle, which we will shade.

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Draw the graph of the following equations : x+y=5x + y = 5x+y=5, x−y=5x - y = 5x−y=5, and (i) find the solution of the equations from the graph. (ii) shade the triangular region formed by the lines and the y-axis.