Mabel was asked whether the following equation is an identity: (4x - 3)(x - 2)2 = 4x3 – 19x2 + 4x - 12 - She performed the following steps: (4x - 3)(x - 2)2 - - Step 1 (4x – 3)(x - 2)(x - 2) Step (4x - 3)(x2 - 2x - 2x + 4) II Step 3 = (4x – 3)(x2 - 4x + 4) Step 4 423 – 16x2 + 16x – 3.xº - 12x – 12 Step 5 4x3 – 19x2 + 4x – 12 For this reason. Mabel stated that the equation is a true identity, Fit

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24