Lesson 10.7: Help for Exercises 60-62 on page 637
In Exercise 60, use the location of East High School as the origin. Then determine the coordinates where Clark Street intersects State Street (on the y-axis) and Main Street (on the x-axis). Knowing these two points, you can determine the equation of the line represented by Clark Street. Find the equation of the circle knowing that it is centered 2 miles away from the origin on the xaxis and has a radius of 1 mile. Use the substitution method to find the location of the points of intersection between the circle and the line. The distance between these two points of intersection is the portion of Clark Street for which residents are not eligible to ride the bus
In Exercise 61, if the ship's location is north and east of the origin, then it lies in the first quadrant, so consider only positive values of x and y. You can solve the first equation for either variable and use the substitution method in the second equation. The result of substitution will be a fourth degree polynomial. Treat this polynomial as a quadratic equation and solve for a variable squared by factoring. Then apply the square root property, followed by substitution, to solve for the remaining variable. Again, remember that x and y must be positive.
In Exercise 62, as in Exercise 61, the intersection point of the line and the hyperbola occurs in the first quadrant. Restrict values of x and y to only positive numbers. Youšll need to find the equation of the line passing through points (0, 8) and (10, 0). This system should also be solved by the substitution method. A quadratic equation will result. Once this quadratic equation is found (which will take several steps), you will find that its solution is best approached by applying the quadratic formula.