Using graphical method solve the simultaneous equation 2p+2q=2 and 5p-3q=29

Answer 1

To solve the simultaneous equations graphically, we will plot the two given equations on the same coordinate plane and find the point where they intersect.

First, let's solve for each equation separately to find their slopes and y-intercepts.

For the equation 2p + 2q = 2:
- Solving for q:
2q = 2 - 2p
q = 1 - p/2

For the equation 5p - 3q = 29:
- Solving for q:
3q = 5p - 29
q = (5/3)p - 29/3

Now we can plot the graphs of these equations:

For the equation 2p + 2q = 2:
Let's choose arbitrary values of p to solve for q:
When p = 0: q = 1 - 0/2 = 1
When p = 2: q = 1 - 2/2 = 1 - 1 = 0

So the first equation gives us the points (0, 1) and (2, 0).

For the equation 5p - 3q = 29:
Let's choose arbitrary values of p to solve for q:
When p = 0: q = (5/3)(0) - 29/3 = -29/3
When p = 6: q = (5/3)(6) - 29/3 = (5*6 - 29)/3 = 11/3

So the second equation gives us the points (0, -29/3) and (6, 11/3).

Now we can plot these points and draw the lines passing through them:

The first equation:
(0, 1)
(2, 0)

The second equation:
(0, -29/3)
(6, 11/3)

After plotting the lines, we can see that they intersect at the point (4, -1/2).

Therefore, the solution to the simultaneous equations 2p + 2q = 2 and 5p - 3q = 29 is p = 4 and q = -1/2.