Download MAT 090 Basic Algebra Quiz 4 Solutions DIRECTIONS. Partial credit

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