Question

Using graphical method to solve the simultaneous equation y-2x+1=0 and 2y+x-8=0

Answer 1

To solve the simultaneous equations using graphical method, we graph the two equations on the same coordinate plane and find the point of intersection, which represents the solution to the equations.

1. Begin by rewriting the equations in slope-intercept form (y = mx + b):
Equation 1: y - 2x + 1 = 0
Rewrite as: y = 2x - 1
Equation 2: 2y + x - 8 = 0
Rewrite as: y = -0.5x + 4

2. Plot the graphs of both equations on the coordinate plane:
Equation 1 can be plotted by starting at the y-intercept (0, -1) and using the slope 2 to find another point. For example, when x = 1, y = 2(1) - 1 = 1, so you have the second point as (1, 1).
Equation 2 can be plotted by starting at the y-intercept (0, 4) and using the slope -0.5 to find another point. For example, when x = 1, y = -0.5(1) + 4 = 3.5, so you have the second point as (1, 3.5).

3. Plot the points and draw the lines for the equations on the coordinate plane.

4. Find the point of intersection: By examining the graph, you can see that the lines intersect at the point (3, 5).

5. Therefore, the solution to the simultaneous equations is x = 3 and y = 5.