Using graphical method solve the simultaneous equation 2p+2q=2 and 5p-3q=29
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.
To solve the simultaneous equations 2p + 2q = 2 and 5p - 3q = 29 graphically, we will plot the lines represented by each equation on a graph and find their point of intersection, which will give us the solution.
Step 1: Rewrite the equations in slope-intercept form (y = mx + b):
- Equation 1: 2p + 2q = 2
Divide both sides by 2:
p + q = 1
q = 1 - p
- Equation 2: 5p - 3q = 29
Subtract 5p from both sides and then divide by -3:
-3q = -5p + 29
q = (5/3)p - 29/3
Step 2: Draw the graph of each equation on the same set of axes.
For Equation 1:
- Let's choose arbitrary values for p and find q using the equation q = 1 - p.
- Let's choose p = 0
q = 1 - 0 = 1
- Let's choose p = 1
q = 1 - 1 = 0
- Plot the points (0, 1) and (1, 0) on the graph, and draw a straight line through these points. This line represents Equation 1.
For Equation 2:
- Let's choose arbitrary values for p and find q using the equation q = (5/3)p - 29/3.
- Let's choose p = 0
q = (5/3)(0) - 29/3 = -29/3 ≈ -9.67
- Let's choose p = 3
q = (5/3)(3) - 29/3 = 10 - 29/3 = 1/3 ≈ 0.33
- Plot the points (0, -9.67) and (3, 0.33) on the graph, and draw a straight line through these points. This line represents Equation 2.
Step 3: Identify the point of intersection.
- The point where the two lines intersect is the solution to the simultaneous equations.
- From the graph, we can see that the lines intersect at the point (2, -1).
Step 4: Determine the values of p and q.
- From the point of intersection, we can read off the values:
p = 2
q = -1
So, the solution to the simultaneous equations is p = 2 and q = -1.
To solve the simultaneous equation 2p + 2q = 2 and 5p - 3q = 29 using the graphical method, follow these steps:
Step 1: Solve for p in terms of q in the first equation.
Rewrite the first equation as:
p = (2 - 2q) / 2
Simplify further:
p = 1 - q
Step 2: Plot the graphs of the two equations on the same coordinate system.
Let's assign the x-axis to represent the values of p and the y-axis to represent the values of q.
For the first equation, we can create a table of values for q and calculate the corresponding values of p:
q | p = 1 - q
---------------
0 | 1
1 | 0
2 | -1
3 | -2
Plot these points on the graph.
For the second equation, similarly create a table of values for q and calculate the corresponding values of p:
q | p = (29 + 3q) / 5
-----------------------
0 | 5.8
1 | 4.4
2 | 3.0
3 | 1.6
Plot these points on the graph as well.
Step 3: Analyze the graph to find the point of intersection.
Look for the point on the graph where the two lines intersect. This represents the common solution which satisfies both equations.
Step 4: Read the coordinates of the intersection point.
Once you have identified the point of intersection, read the values of p and q at that point.
The coordinates of the intersection point provide the solution to the simultaneous equations.
In this case, the two lines will intersect at the point (-3, 4). Therefore, the solution to the simultaneous equations 2p + 2q = 2 and 5p - 3q = 29 is p = -3 and q = 4.