Question

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

x - 15 = 5 or 2x + 5 = 1
b. Write a different system of equations that would have the same solution set.

Answer 1

Explanation:

`x-15=5`

`2x+5=1`

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

`2x=1-5\\\Rightarrow x=(-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+(3)/(4)=25\\\Rightarrow y=25-(3)/(4)\\\Rightarrow y=24.25`

Answer 2

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

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

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