Question

Without graphing, classify the system of equations as either consistent or inconsistent. −2x+3y=10 and y=2x/3+10/3

Answer 1

The system of equations is inconsistent.

Step-by-step explanation:

To classify the system of equations without graphing, we can solve the equations simultaneously. The given system of equations is:

-2x + 3y = 10

y = 2x/3 + 10/3

To solve this, we can substitute the second equation into the first equation:

-2x + 3(2x/3 + 10/3) = 10

-2x + 2x + 20/3 = 10

20/3 = 10

This is a contradiction, since 20/3 is not equal to 10. Therefore, the system of equations is inconsistent.