Question

Solve the following system of linear equations graphically.

4x - 5y - 20 = 0,
3x + 5y - 15 = 0,
Determine vertices of the triangle formed by the line representing the above equation and the y-axis. Find the area of the triangle so formed.
a) Triangle vertices: A(0, 4), B(5, 0), C(5, 3)
b) Area of the triangle = 10 square units
c) The triangle is right-angled.
d) The lines are parallel.

Answer 1

To solve the system of linear equations graphically, rearrange the equations in slope-intercept form, plot their graphs, find the intersection point, determine the triangle vertices on the y-axis, and calculate the area of the triangle.

Step-by-step explanation:

To solve the system of linear equations graphically, we need to graph both equations and find the intersection point.

1. Start by rearranging both equations in slope-intercept form, y = mx + b.
2. Plot the graph of each equation on the same coordinate plane.
3. Find the intersection point, which represents the solution to the system of equations.
4. The three vertices of the triangle formed by the line representing the equations and the y-axis are A(0,4), B(5,0), and C(5,3).
5. To find the area of the triangle, we can calculate the base and height of the triangle. The base is the distance between points B(5,0) and C(5,3), which is 3 units. The height is the y-coordinate of point A, which is 4 units. The area of the triangle is given by the formula: Area = 1/2 * base * height = 1/2 * 3 * 4 = 6 square units.