Part a: create a system of linear equations with no solution. in two or more complete sentences, explain the specific characteristics that you included in each equation to ensure that the system would not have a solution. part b: using one of the equations that you created in part a, create a system of linear equations that has one solution (x, y). use substitution to solve the system.

Part A:

y = 2x + 3

y = 2x - 1

When creating a system of linear equations with no solution, I created a pair of equations whose lines have the same slope. The lines will be parallel and having the same slope ensures that the lines will not overlap. I also made sure that the y-intercepts of each equation were different because if they were the same, the solution would be infinitely many instead of no solution.

Part B:

y = 2x + 3

y = 2x - 1

2x + 3 = -2 - 1

4x = -4

x = -1

y = 2(-1) + 3

y = -2 + 3

y = 1

(-1, 1)

Step-by-step explanation:

Part A.

You need two equations with the same slope and different y-intercepts.

Their graph is parallel lines. Since the lines do not intersect, there is no solution.

y = 2x + 2

y = 2x - 2

Part B.

We use the first equation as above. For the second equation, we use an equation with different slope. Two lines with different slopes always intersect.

y = 2x + 2

y = -2x - 2

In the second equation, y = -2x - 2. We now substitute -2x - 2 for y in the first equation.

-2x - 2 = 2x + 2

-4x = 4

x = -1

Now substitute -1 for x in the first equation to find y.

y = 2x + 2

y = 2(-1) + 2

y = -2 + 2

y = 0

Solution: x = -1 and y = 0