# SOLUTION: Solve the following system of equations algebraically: 9x^2 + y^2 = 9 3x – y = 3

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 Question 66010: Solve the following system of equations algebraically: 9x^2 + y^2 = 9 3x – y = 3Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!```Solve the following system of equations algebraically: 9x² + y² = 9 3x – y = 3 Let's do it algebraically and then check it graphically: Solve the second equation for y 3x – y = 3 -y = 3 - 3x Multiply through by -1 y = -3 + 3x Save one sign by swapping terms y = 3x - 3 Substitute into the 1st equation: 9x² + y² = 9 9x² + (3x - 3)² = 9 9x² + (3x - 3)(3x - 3) = 9 9x² + 9x² - 9x - 9x + 9 = 9 18x² - 18x + 9 = 9 18x² - 18x = 0 Factor out 18x 18x(x - 1) = 0 Set each factor = 0 18x = 0 gives x = 0 x - 1 = 0 gives x = 1 For each of those solutions for x, we must find a corresponding solution for y: To find this we substitute into y = 3x - 3 For x = 0, y = 3(0) - 3 y = -3 So one solution is (x, y) = (0, -3) For x = 1, y = 3(1) - 3 y = 0 So the other solution is (x, y) = (1, 0) This means the two graphs would have two points of intersection. The graph of 9x² + y² = 9 is this oval shaped graph, called an ellipse: and the graph of 3x – y = 3 is this line which crosses it twice: Notice that the graphs cross at the points (1, 0) and (0, -3) Edwin```