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Bruce studied this system of equations:
( 3x + 2y = 12
x-y = 4
He found that another system of equations had the same solution:
6x + 4y = 24
x-y = 4
Without solving the systems of equations, how can Bruce tell that they both have the same solution?

A.Both systems include x-y=4

B .The two systems use the same two variables.

C . all the coefficients of both systems are integers

D . both equations in the second system are multiples of the equation in the first system

Respuesta :

mathman816

Answer:

Answer:D. if you can select two answer, then do A and D but D is more accurate

boffeemadrid

It is required to know whether the given set of equations have the same solution.

The correct option is D . both equations in the second system are multiples of the equation in the first system

The equations are

[tex]3x+2y=12[/tex]

[tex]x-y=4[/tex]

[tex]6x+4y=24[/tex]

[tex]x-y=4[/tex]

The equation [tex]6x+4y=24[/tex] can be written as

[tex]2(3x+2y)=24\\\Rightarrow 3x+2y=\dfrac{24}{2}\\\Rightarrow 3x+2y=12[/tex]

So, the equations [tex]3x+2y=12[/tex] and [tex]6x+4y=24[/tex] are equivalent.

And the equation [tex]x-y=4[/tex] is same in both the sets.

So, the given equations have the same solution.

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