Can i get some help

Question

Question 1: Classify the system and identify the number of solutions.

x − 2y + z = −7

x − 5y − z = −5

x − 8y − 3z = −3

A.) consistent, independent; one

B.) inconsistent; none

C.) consistent, dependent; none

D.) consistent; dependent; infinite

Question 2: Let g(x) be the transformation of f(x) = |x| down 3 units. Identify the rule for g(x) and its graph.

A.) g(x) = |x − 3|

B.) g(x) = |x| − 3

C.) g(x) = |x| − 3

D.) g(x) = |x − 3|

Question 3: Identify the graph that represents the given system of inequalities and the classification of the figure created by the solution region.

A.) triangle

B.) quadrilateral

C.) triangle

D.) quadrilateral

Please just only give solution and explanation.

Answer 1

1. D consistent, dependent infinite solutions
2. B shifted down by 3
3. A. x>-1 is only represented in A

Answer 2

1

x − 2y + z = −7

x − 5y − z = −5

x − 8y − 3z = −3

1 -2 1

1 -5 -1

1 -8 -3

has determinant 0

This eliminates solutions A and C,

If you subtract equation 3 from equation 1, you get

6y + 4z = -4

If you subtract equation 3 from equation 2, you get

3y + 2z = -2

One equation is a multiple of the other.

Thus, the equations are consistent.

This tells us that D is the answer. We could stop here, but let's find the answer.

3/2y + z = -1

x − 2y + z = −7

Subtracting, 7/2y - x = 6

Let y = 0; then x = -6 and z = -1

Note how (-6, 0, -1) solves each of the 3 equations.

As we have a point and the two equations 3y + 2z = -2, 7y - 2x = 12, the equation of the line is

(-6, 0, -1) + (7, 2, -3) t

Try t = 1

(1, 2, -4)

You will see that it fits both lines.

2.

(0, 0) is on y = |x|

Move down 3, and you have (0, -3)

Only b has this value. Also, note that y = |x| is moved down 3 by y = |x| - 3, which is the equation provided.

1. You could find the points that are the intersection of the 3 lines (of course, this is a triangle). You could also note that only one triangle has |x| = -1. A