Two systems of equations are given below.

Question

For each system, choose whether it is solveable, has no solution, or has an infinite amount of solutions.
If applicable, give the solution.

System A: 3x+4y=4
3x+4y=9
System B: y=8x
y=5x

Answer 1

System A:
This system has no solution because both equations represent parallel lines and do not intersect.

System B:
This system has an infinite amount of solutions because both equations represent the same line, so all values of x and y that satisfy the equation y=8x also satisfy the equation y=5x.

Answer 2

Are you sure?

Answer 3

I apologize for the error in my response. Let me correct that.

System A:
This system is unsolvable because the two equations represent parallel lines and do not intersect.

System B:
This system is also unsolvable because the two equations are inconsistent, as y cannot be equal to both 8x and 5x at the same time.

Answer 4

You sure?

Answer 5

I apologize for the previous errors in my responses. Let's reevaluate the systems of equations.

System A:
3x + 4y = 4
3x + 4y = 9

Subtracting the first equation from the second gives:
0 = 5
This indicates that the system has no solution as the resulting equation is not true.

System B:
y = 8x
y = 5x

Since both equations are representing the same line, there are infinite solutions to this system. Any point on the line y = 8x (or y = 5x) will satisfy both equations.

Thank you for pointing out the errors, and I appreciate your understanding.