| Directions: In each of the following questions two equations are given, solve these equations and give answer. [IBPS (PO) 2013] |
| I. \[2x+3y=14\] |
| II. \[4x+2y=16\] |
A) If \[x\ge y\]
B) If \[x>y\]
C) If \[x\le y\]
D) If \[x<y\]
E) If \[x=y\]
Correct Answer: D
Solution :
| We have, \[2x+3y=14\] ... (i) |
| and \[4x+2y=16\] ... (ii) |
| On multiplying Eq. (i) by 2 and then subtract Eq. (ii) from this, we get |
| \[4x+6y-\,\,(4x+2y)=28-16\] |
| \[\Rightarrow \] \[6y-2y=12\]\[\Rightarrow \]\[4y=12\] |
| \[\therefore \] \[y=\frac{12}{4}=3\] |
| From Eq. (i), |
| \[2x+3\,\,(3)=14\] |
| \[\Rightarrow \] \[2x=14-9\]\[\Rightarrow \]\[2x=5\] |
| \[\therefore \] \[x=\frac{5}{2}\] |
| Hence, \[y>x\] |
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