x^2 + 4y^2 = 100 ____1 4y - x^2 = -20 ____2 Add both 1 & 2 together. x^2 gets cancelled 4y^2 + 4y = 80 (send 80 to the other side and divide by 4) Then equation the becomes : y^2 + y -20 =0 Now factorise the equation: (y+5) (y-4) = 0 Solve for y : y = -5 and y = 4 Using the values of y to find the values of x. From equation 1: x^2 = 100 - 4y^2 x = /100 - 4y^2 (/ means square root) Replace values of y y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0 y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6 Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
