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What value of b will cause the system to have an infinite number of solutions?

A system of equations. y equals 6 x plus b. negative 3 x plus StartFraction one-half EndFraction y equals negative 3.

A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes through the points (1, 0) and (0, negative 6).

-6
-3
3
6

Respuesta :

Answer:

-6 on edge

Step-by-step explanation:

facundo3141592

The value of b that causes the system of equations to have infinite solutions will be: b = -6

System with infinite solutions:

A system of linear equations will have infinite solutions only when both equations represent the same line.

In this case our equations are:

y = 6x + b

-3x + (1/2)*y = -3

So the value of b needs to be such that these two equations are equal

Let's isolate y in the second equation:

(1/2)*y = -3 + 3x

y = -3*2 + 3x*2 = -6 + 6x

Then we must have:

6x - 6 = 6x + b

-6 = b

Thus, the value of b that causes the system to have infinite solutions is b = -6.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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