Given equations A and B as 2/5x+y=12 and 5/2y-x=6 respectively which expression will eliminate the variable X a) 5/2A+2/5B b)5/2A-B c) A+ 2/5B D ) 5/2A-2/5B E) 25/10A+6/10B

Given equations A and B as 25xy12 and 52yx6 respectively which expression will eliminate the variable X a 52A25B b52AB c A 25B D 52A25B E 2510A610B class=

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Answer:

C) [tex]A+\frac{2}{5}B[/tex]

Step-by-step explanation:

Given Equations:

A) [tex]\frac{2}{5}x+y=12[/tex]

B) [tex]\frac{5}{2}y-x=6[/tex]

In order to eliminate [tex]x[/tex] we need to multiply [tex]\frac{2}{5}[/tex] to equation B and add it to A.

Multiplying [tex]\frac{2}{5}[/tex] to B.

⇒ [tex]\frac{2}{5}\times (\frac{5}{2}y-x)=\frac{2}{5}\times 6[/tex]

⇒ [tex](\frac{2}{5}\times\frac{5}{2}y)-(\frac{2}{5}x)=\frac{12}{5}[/tex]

⇒ [tex]y-\frac{2}{5}x=\frac{12}{5}[/tex]

Adding it equation A.

   [tex]\frac{2}{5}x+y=12[/tex]

+ [tex]-\frac{2}{5}x+y=\frac{12}{5}[/tex]

We get [tex]2y=\frac{72}{5}[/tex]

Thus [tex]x[/tex] is eliminated.

So, the expression used to eliminate [tex]x[/tex] is:

[tex]A+\frac{2}{5}B[/tex]

Answer:

c

Step-by-step explanation:

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