Answer:To solve the simultaneous linear equations 3x - 4y = 25 and 4x - yz = 16 using the graphical method, we can follow these steps:
1. Solve for y in the first equation:
3x - 4y = 25
-4y = -3x + 25
y = (3/4)x - (25/4)
2. Solve for z in the second equation:
4x - yz = 16
yz = 4x - 16
z = (4x - 16)/y
3. Choose a range of x values to plot on a graph. Let's say x ranges from -10 to 10.
4. Substitute the chosen x values into the equations to find the corresponding y and z values. For example, when x = -10:
y = (3/4)(-10) - (25/4) = -30/4 - 25/4 = -55/4
z = (4(-10) - 16)/(-55/4) = (-56)/(-55/4) = 224/55
5. Repeat step 4 for other selected x values.
6. Plot the points (x, y) and (x, z) on the graph.
7. Connect the points with straight lines to form the graphs of the equations.
8. Locate the point where the two lines intersect. This point represents the solution to the simultaneous equations.
9. Read the coordinates of the intersection point, which represent the values of x, y, and z that satisfy both equations.
It's important to note that the graphical method may not provide an exact solution, especially when the lines are close or parallel. In such cases, additional methods like substitution or elimination can be used to find a more precise solution.
Explanation: