Quadratic/Linear Systems of Equation

Question

A rocket is launched from the ground and follows a parabolic path represented by the equation `y=-x^{2}+10x` where x represents time in (seconds) and y represents the height in (meters). At the same time, a flare is launched from a height of 10 feet and follows a straight path represented by the equation `y=-x+10.\ \ `

a) At what time does the rocket and the flair intersect in the air?

b) What is the height when this happens?

Answer 1

-x^2 + 10 = -x +10

-x^2 +x = 0

x(-x+1) = 0

at x= 0 and x= 1 seconds, they are at an equal height

y = 10 and 9 meters