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Which statement describes the solution to the system of equations?



A.-) The system has exactly one solution.

B.- The system has exactly two solutions.

C.-) The system has no solutions.

D.-) The system has infinitely many solutions.

Respuesta :

danielmaduroh

For this case:

D.-) The system has infinitely many solutions.

Explanation:

Remember that you have to write complete questions in order to find exact and good answers. In this exercise, the system is missing. However, I'll provide the following system:

[tex]\text{\ensuremath{\left.\begin{array}{c}(1)\\(2)\end{array}\right.\left\{ \begin{array}{c}3x+y=-6\\6x+2y=-12\end{array}\right.}}[/tex]

So we have two equations and two variables. Our first equation is:

[tex]3x+y=-6[/tex]

And the second equation is:

[tex]6x+2y=-12[/tex]

When graphing these two lines, we can get the following possibilities:

  • They have a unique solution. This means the graphs intersect at a single point.
  • They have infinitely many solutions. This implies the lines are basically the same.
  • They have no solution. This implies they are parallel but with different y-intersect.

By dividing equation (2) by 2 we get:

[tex]\frac{6x+2y}{2}=\frac{-12}{2} \\ \\ 3x+y=-6[/tex]

So we get the same equation as line (1), so the conclusion is that they have infinitely many solutions.

Learn more:

Infinitely many solutions: https://brainly.com/question/13771057

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Answer:

Infinitely many solutions

Step-by-step explanation:

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