Ingrid
12th Grade
Student

The question says find the points of intersection of the graphs of the equation, and check your results analytically.

x squared + y squared=25
2x+ y=10

Thank you for your help ahead of time.

Hi Ingrid.

What the question means is:

1. Draw a graph of the circle x² + y² = 25 (that's a circle with radius five centered on the origin) and on the same graph, draw the line 2x + y = 10. See where the lines cross. Those are your points of intersection. This first part of the question calls for your judgement in drawing and reading the graph properly.
   
   
2. Figure it out analytically. The way to do this is to re-arrange the second equation to solve for either y or x (let's say y). Then you can substitute this value of y in for y in the first equation, so you will end up with a quadratic equation with just the variable x in it. If you use the quadratic formula, you'll find the possible values of x. Then, for each value of x, you just put it into the second equation to find the corresponding value of y. That gives you the exact co-ordinates of intersection.

Hope this helps,
Stephen La Rocque.