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

Answer 1

To solve the simultaneous equations graphically, we will plot the two lines represented by the equations and find their point of intersection.

First, let's rewrite the equations in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Equation 1: y - 2x + 1 = 0
Rearrange the equation to isolate y:
y = 2x - 1

Equation 2: 2y + x - 8 = 0
Rearrange the equation to isolate y:
2y = -x + 8
Divide by 2:
y = -1/2x + 4

Now, we can plot these lines on a graph:

- First, plot the y-intercept of Equation 1, which is -1 (b=-1). Then, use the slope of 2 (m=2) to find another point on the line. This can be done by moving 2 units up and 1 unit to the right from the y-intercept point. Connect the two points to draw the line. (Line 1)

- Second, plot the y-intercept of Equation 2, which is 4 (b=4). Then, use the slope of -1/2 (m=-1/2) to find another point on the line. This can be done by moving 1 unit down and 2 units to the right from the y-intercept point. Connect the two points to draw the line. (Line 2)

The two lines will intersect at a point, which will be the solution to the simultaneous equations.

Here is the graph of the two lines:
(insert graph with Line 1: y = 2x - 1 and Line 2: y = -1/2x + 4)

The point of intersection is the solution to the simultaneous equations. By examining the graph, it appears that the lines intersect at approximately (3, 5).

Therefore, the solution to the simultaneous equations y - 2x + 1 = 0 and 2y + x - 8 = 0 is x = 3 and y = 5.