In Example 7, change the coefficient of y in the first equation to 3.

Data from Example 7

In a computer game, two rockets follow paths described by the equations x² = 2y and 3x − y = 5. Determine if the rocket paths ever cross. Solving the equation of the path of the first rocket, we get y = 0.5x². This parabola has its vertex at the origin and opens upward since a > 0. This means there cannot be a point of intersection for y

The straight line rocket path has intercepts of (0.00, −5.00) and (1.67, 0.00). This means any possible point of intersection must be in the first quadrant. Therefore, we have the window settings as shown in Fig. 14.8. From the figure, we see that the two rocket paths do not cross. Mathematically, this means that the curves do not intersect and that there are no real solutions to this system of equations.

NORMAL FLOAT AUTO REAL RADIAN MP 12, o 0 Fig. 14.8