Question

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

Answer 1

Answer:

C) $A+\frac{2}{5}B$

Step-by-step explanation:

Given Equations:

A) $\frac{2}{5}x+y=12$

B) $\frac{5}{2}y-x=6$

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

Multiplying $\frac{2}{5}$ to B.

⇒ $\frac{2}{5}\times (\frac{5}{2}y-x)=\frac{2}{5}\times 6$

⇒ $(\frac{2}{5}\times\frac{5}{2}y)-(\frac{2}{5}x)=\frac{12}{5}$

⇒ $y-\frac{2}{5}x=\frac{12}{5}$

Adding it equation A.

   $\frac{2}{5}x+y=12$

+ $-\frac{2}{5}x+y=\frac{12}{5}$

We get $2y=\frac{72}{5}$

Thus $x$ is eliminated.

So, the expression used to eliminate $x$ is:

$A+\frac{2}{5}B$