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SAT® Math

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Moderate

Infinitely Many Solutions

SATMAT-JIUFK7

$ \begin{cases}5x-\frac{1}{5}y=3-C\\\ 10x-\frac{9}{10}y=\frac{3}{2}-\frac{1}{2}y \end{cases} $

If the system of equations shown above has infinitely many $ \left( x,y \right) $ solutions, then find the value of the constant C.

(No Calculator)

A

$ 1\cfrac { 1 }{ 2 } $

B

$ 2\cfrac { 1 }{ 4 } $

C

$ 3\cfrac { 3 }{ 4 } $

D

All of these are possible values for $ C $ in this system.