Answer:
Step-by-step explanation:
Verifying Bernard's Location:
Bernard's coordinates: (50, -75)
Equation for Bernard's road: y = 1/2 * x - 100
Verification:
Substitute Bernard's x-coordinate (50) into the equation:
y = (1/2) * 50 - 100
Simplify:
y = 25 - 100
y = -75
Result:
Since Bernard's y-coordinate (-75) matches the result obtained from the equation (-75), we can verify that Bernard is indeed on the road represented by the equation y = 1/2 * x - 100.
Finding the Intersection Point:
The intersection point represents the coordinates where the two roads meet. We can find this point by solving the system of equations formed by the two road equations. Here are two methods to achieve this:
Method 1: Substitution
Solve one equation for y in terms of x (preferably the simpler equation).
Substitute this expression for y in the other equation.
Solve the resulting equation for x (the x-coordinate of the intersection point).
Substitute the obtained x value back into either original equation to solve for y (the y-coordinate of the intersection point).
Method 2: Elimination
Try to manipulate the equations algebraically to get one of the variables (x or y) cancelled out.
Solve the resulting equation for the remaining variable.
Substitute this value back into either original equation to solve for the other variable.
Using either method, you will find that the coordinates of the point of intersection are:
(x, y) = (340, 70)