Solve the following system over the set of real numbers: x + 2y = 1, x^2 + 4y^2 = 25

Answer 1

If you substitute x = 1 - 2y into the x term in the second expression, you end up with a quadratic expression in terms of y. Solve this expression (hint: if there is a common factor with all terms, divide through by this first; you can then easily factor).

Once you find the 2 values for y that solve the quadratic, you can plug each into x=1 - 2y to solve for x.

Note: if you draw the ellipse and line, you will see that the line crosses the ellipse in 2 points. In fact, a careful drawing of the ellipse will show the two solutions.