Question

Please help asap 

For the graph shown, select the statement that best represents the given system of equations.
algebra unit 8 lesson 1 assessment question 4
2y – 3x = 9
4y + 3x = 12

A.
coincident

B.
not enough information

C.
inconsistent

D.
consistent and independent

Answer 1

The equtaion has only one solution because they cut each other only once and the are independent ..as both line are different. So it would be (d) consistent and independent

Answer 2

Answer: D. consistent and independent

Explanation:

The given system is
`2y-3x=9\\4y+3x=12`

When we compare the coefficients of the corresponding variables of both the equations we get,

For y,
`(2)/(4)=(1)/(2)`

For x,
`(-3)/(3)=-1`

And
`(1)/(2)\\eq-1`,

⇒ The system in independent.

Therefore the system has one unique solution.

Since, if a system has a unique solution then the system is consistent .

Therefore, the system is consistent and independent.