Question

A. Solve the system, and graph the solution set on a number line.

Answer 1

Answer:

a. the solution set is {-2, 20}

b. 2*x - 30 = 10 or 4*x + 10 = 2

Step-by-step explanation:

a.  Given the system:

x - 15 = 5   or  2*x + 5 = 1

The solution for the first part is:

x - 15 = 5

x - 15 + 15 = 5 + 15

x  = 20

The solution for the second part is:

2*x + 5 = 1

2*x + 5 - 5 = 1 - 5

2*x = -4

x = -4/2

x = -2

So the solution set is {-2, 20}, see the picture attached.

b. If you multiply both sides of the equations of the system by a constant,  like 2, you will get a new system with the same solution as the original.

2*(x - 15) = 2*5  

2*x - 30 = 10

2*(2*x + 5) = 2*1

4*x + 10 = 2

Then, the new system is:

2*x - 30 = 10 or 4*x + 10 = 2

Answer 2

Step-by-step explanation:

$x-15=5$

$2x+5=1$

$x=5+15\\\Rightarrow x=20$

$2x=1-5\\\Rightarrow x=\frac{-4}{2}\\\Rightarrow x=-2$

The two equations are lines on the x axis and they do not intersect hence they have no solution.

Any other parallel lines will have no solution

For example

$y-10=4\\\Rightarrow y=14$

$y+\frac{3}{4}=25\\\Rightarrow y=25-\frac{3}{4}\\\Rightarrow y=24.25$