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Aim: How do we solve systems of equations algebraically?

Aim: How do we solve systems of equations algebraically?. Do Now: Solve the system of linear equations x – 2 y = 4 y = 3 – 2 x. (2,-1). HW: p.237 # 20,22,24,28,30,34, # 38- 43. Solve the system: y = 2 x +1 y = x 2 + 4 x + 1.

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Aim: How do we solve systems of equations algebraically?

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  1. Aim: How do we solve systems of equations algebraically? Do Now: Solve the system of linear equations x – 2y = 4 y = 3 – 2x (2,-1) HW: p.237 # 20,22,24,28,30,34, # 38- 43

  2. Solve the system: y = 2x +1 y = x2 + 4x + 1 Replace y in 2nd equation by 2x + 1 2x + 1 = x2 + 4x + 1 Move all the terms to one side of the equation x2 + 2x = 0 Solve for x x (x + 2) = 0 x = 0, x = – 2 Substitute 0 and – 2 in 1st equation y = 2(0) + 1 = 1 y = 2(-2) + 1 = – 3 (0,1) (-2,-3) (0,1) (-2,-3)

  3. Solve the system: x2 + 4y2 = 4 x = 2y – 2 Replace x in 1st equation by 2y – 2 (2y – 2)2 + 4y2 = 4 Multiply and simplify the equation (2y – 2)(2y – 2) + 4y2 = 4 4y2 – 8y + 4 + 4y2 = 4 8y2 – 8y = 0 8y(y – 1) = 0, y = 0, y = 1 Solve for y Replace y into 2nd equation x = 2(0) – 2 = - 2 x = 2(1) – 2 = 0 (-2,0)(0,1) (-2,0) (0,1)

  4. Solve the system algebraically: y = x2 – 4 y = – 2x Replace y in 1st equation by – 2x The equation is not factorable, then use the formula Replace x into the 2nd equation to find y and

  5. A circle centered at (0, 0) with radius square root of 10 A line with slope 1 and y int. 2 Let’s identify and graph each of these equations. What do they look like? From the second equation we know what y equals so let’s sub it in the first equation. FOIL this

  6. (1, 3) (-3, -1)

  7. 1. Solve the system: y = x2 – 8x + 15 y = – x + 5 (2,3) (5,0) 2. Solve the system: xy = – 6 x + 3y = 3 (-3,2) (6,-1) 3. Solve the system: x2 – 2y2 = 11 y = x + 1

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