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]
