Question

"Two cars, A and B, are moving towards each other. Car A is decelerating with the line y^1 = -x + 3, and car B is accelerating with the line y^2 = x - 1. Determine the coordinates (x, y) at which the two cars will meet. Show your working."

Answer 1

The coordinates where cars A and B will meet based on their equations y¹ = -x + 3 and y² = x - 1 are (2, 1), found by solving the system of equations.

Step-by-step explanation:

The student asks to determine at which coordinates the cars A and B will meet based on their represented lines in a coordinate system. This can be interpreted as finding the point of intersection between the two lines, y¹ = -x + 3, and y² = x - 1.

The first step is to set the equations equal to each other since the cars meet at the same point, and thus this point will have the same y-coordinate for both equations.
- x + 3 = x - 1

By solving this equation, we find:

2x = 4

x = 2

Then, we substitute x back into either of the original equations to find y. Using y²:

y = 2 - 1

y = 1

The coordinates at which the two cars will meet are (2, 1).