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Download MAT 090 Basic Algebra Quiz 4 Solutions DIRECTIONS. Partial credit
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MAT 090 Basic Algebra Quiz 4 Solutions DIRECTIONS. Partial credit will only be given where there is a clear explanation offered for an answer (i.e., work shown). 1. Is the pair (6, −8) a solution to the following system of equations? Explain. −2y = x + 10 3y = 2x + 30 Answer: Plugging into the first equation gives (−2)(−8) = 6 + 10, which simplifies to the true statement 16 = 16, so (6, −8) satisfies the first equation. Plugging into the second equation gives (3)(−8) = (2)(6) + 30, which simplifies to the false statement −24 = 42. Since (6, −8) does not satisfy both equations, it is not a solution to the system. 2. Estimate the solution to the following system of equations by graphing. 2x − 3y = −6 y = −3x + 2 Answer: Based on the graph below, I would estimate the solution to be (0, 2). 1 2 x - 3 y - 6 and y 2 - 3 x 15 10 5 -4 -2 2 4 -5 -10 3. Without graphing the lines, explain why the following system has no solution. 5x + 4y = 7 10x + 8y = 4 5 7 Answer: The first line is equivalent to y = − x + and so has slope 4 4 5 5 1 − . The second line is equivalent to y = − x + and also has slope 4 4 2 5 − . Since the lines have different y−intercepts, they are parallel, so 4 the system has no solution. 4. Solve the following system of equations by substitution. 3x + 4 = −y 2x + y = 0 Answer: From Equation 1, we have y = −3x−4. Substituting this into the second equation gives 2x + (−3x − 4) = 0 or x = −4. Substituting 2 this back into the second equation gives (2)(−4) + y = 0 or y = 8. Thus, the solution to the system is (−4, 8). 5. Solve the following system of equations by substitution. 4x + 5y = −8 25 − 10y = 8x 4 8 Answer: From equation 1, y = − x − . Substituting this into the 5 5 4 8 second equation gives 25 − 10 − x − = 8x or 25 + 8x − 16 = 8x 5 5 or 9 = 0. We conclude that the system is inconsistent, i.e., there is no solution. 3