Question

Several systems of equations are given below.

System 1
y = 6x – 1.5
y = –6x + 1.5

System 1
x + 3y = –6
2x + 6y = 3

System 1
2x –y = 5
6x – 3y = 15



Which system of equations is consistent-independent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is consistent-dependent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is inconsistent-independent? How many solutions will the system of equations have? Expain your answers.

Answer 1

@SolomonZelman

Answer 2

@jim_thompson5910

Answer 3

If there is a solution to the equations, then they are consistent.
If there is only one solution, they are independent.
If they are the same equation, then they are consistent and dependent.
if they are parallel they are inconsistent.

If you solve for the equations (set one equal to another and solve for x) then you can find out:
y = 6x – 1.5
y = –6x + 1.5

the second line in the equation is the same as the first multiplied by -1.
\[6x - 1.5 = -6x + 1.5\]
\[12x = 3\]
\[x = \frac{3}{12}\]
\[x = \frac{1}{4}\]

this system of equations is consistent and independent.

Now you do the rest.