# SOLUTION: Part 1: Suppose you need to solve a system of equations in which one equation represents a circle and the other represents a line. How many solutions can your system have? Sele

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Part 1: Suppose you need to solve a system of equations in which one equation represents a circle and the other represents a line. How many solutions can your system have? Sele      Log On

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 Click here to see ALL problems on Linear-systems Question 349538: Part 1: Suppose you need to solve a system of equations in which one equation represents a circle and the other represents a line. How many solutions can your system have? Select ALL that are possible. 0,1,2,3,4, infinitely many Part 2: How many solutions does the following system of equations have? x2+y2=64 x=1 0,1,2,3,4, infinitely manyAnswer by Theo(3458)   (Show Source): You can put this solution on YOUR website!one equation represents a circle and the other equation represents a line. you can have 0, 1, or 2 solutions. 0 if the line and the circle never intersect 1 if the line is tangent to the circle. 2 if the line intersects the circle at any other angle. the line can never intersect the circle at more than 2 points. your equation is: x^2 + y^2 = 64 x = 1 this is like solving equations simultaneously to get a common solution. if x = 1, you can substitute in the first equation to get 1 + y^2 = 64 which give you y^2 = 63 which gives you y = +/- sqrt(63). this implies 2 solutions to this equation. The graph of the equation of the circle should confirm this. To graph the equation of the circle, solve for y to get: y = +/- sqrt(64-x^2) that graph is shown below: Draw a vertical line at x = 1 and you will see that the intersection of that vertical line and the circle is around y = +/- 7.937253933. I drew 2 horizontal lines at y = +/- 7.937253933 so you can see that a little easier. when x = 0, y = +/- sqrt(64-0) = +/- sqrt(64) = +/- 8. That's the highest and lowest point of the circle. when x = 1, y = +/- sqrt(64-1) = +/- sqrt(63) = +/- 7.937253933. That's close to the highest point but hot exactly there (just a little below). Solving the 2 equations simultaneously yielded the result.