On a movie set, an archway is modeled by the equation
y = -0.5x2 + 3x, where y is the height in feet and x is the horizontal distance in feet. A laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points A and B. At what height from the ground are the points A and B?
1.5 feet and 3.5 feet
1.5 feet and 4 feet
3.5 feet and 4 feet
4 feet and 4 feet

a full explanation of how to work these out would be nice if possible

Question

On a movie set, an archway is modeled by the equation 
y = -0.5x2 + 3x, where y is the height in feet and x is the horizontal distance in feet. A laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points A and B. At what height from the ground are the points A and B?
1.5 feet and 3.5 feet
1.5 feet and 4 feet
3.5 feet and 4 feet
4 feet and 4 feet

a full explanation of how to work these out would be nice if possible

zzr0ck3r · Answer

Solve the linear equation (the second one) for $y$ and then set the two equations equal to each other, then solve.

vanniedium · Answer

The answer would be 1.5 feet and 4 feet which are the points of intersection for the two equations. I created a step-by-step solution for you at Calorful: http://goo.gl/XtxbNS This is a step by step calculator for algebra questions.