Question

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 A
3x + 2=y
3x=y
This makes the equation impossible, as no number equals itself plus two.
Part B
y=x+2
y=2x
Now, use substitution:
2x=x+2
x=2

Answer 1

To create a system of linear equations with no solution, the equations must represent parallel lines, which have the same slope but different y-intercepts. An example is two equations 3x + 2 = y and 3x + 4 = y, which have no common solution.

Step-by-step explanation:

To create a system of linear equations with no solution, we must ensure that the equations represent parallel lines, which means they have the same slope but different y-intercepts. Here's an example of such a system:

• 3x + 2 = y
• 3x + 4 = y

Both equations have the same slope of 3, but different y-intercepts (2 and 4), which means they are parallel lines that will never intersect. This lack of intersection points signifies that the system has no solution. It's important to notice that no value for x will satisfy both equations simultaneously because, although they change by the same amount with respect to x, they start at different values along the y-axis, indicated by their distinct y-intercepts 2 and 4.