Question

The system of equations shown is solved using the linear combination method

6x-5y=-8 → 6x-5y=-8 + 6x-5y=-8
-24x +20y = 32 + 1 (-24x+ 20y =32) — 6x+5y = 8
0=0
What does 0 = 0 mean regarding the solution to the system?
O
TE
There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line.

Answer 1

Answer: the correct answer is There are infinitely many solutions to the system because the equations represent the same line (D)

Explanation:

Answer 2

Answer: When a system of two linear equations gives an answer of
`0=0`, there are infinitely many solutions. It also means that the graph represents parallel lines, so the answer is the third choice.

Step-by-step explanation: When it comes to systems of equations in algebra, you will see three types of solutions:

1. When you get an exact value & number for x and y, the system has one solution and is consistent/independent.

2. When you get
`0=0` like in this case, the system has infinitely many solutions and is consistent/dependent.

3. When you get numbers that are not equal, for example,
`3\\eq 5`, you have many solutions and the system is inconsistent/independent.