| Column - I | Column - II | ||
| A. | \[2x+y=8\], \[x+6y=15\] | 1. | (3, 4) |
| B. | \[5x+3y=35\], \[2x+4y=28\] | 2. | (4, 5) |
| C. | \[15x+4y=61\] \[4x+15y=72\] | 3. | (3, 2) |
A) A-R, B-P, C-Q
B) A-P, B-R, C-Q
C) A-R, B-Q, C-P
D) None of these
Correct Answer: C
Solution :
| [A] Given, \[2x+y=8\] (i) |
| and \[x+6y=15\] ... (ii) |
| Multiplying Eq. (ii) by 2, we get |
| \[2x+11y=30\] ... (iii) |
| Subtracting Eq. (i) from Eq. (iii), we get |
| \[11y=22\] |
| \[\Rightarrow \,\,\,\,y=2\] |
| From Eq. (i), we get |
| \[2x+2=8\] |
| \[\Rightarrow \,\,\,2x=6\] |
| \[\Rightarrow \,\,\,x=3\] |
| So, \[\left( x,y \right)=\left( 3,2 \right)\] |
| [B] Given, 5x + 3y = 35 ...(i) |
| and 2x+4y=28 ...(ii) |
| On dividing Eq. (ii) by 2, we get |
| \[x+2y=14\] ...(iii) |
| On multiplying Eq. (iii) by 5, we get |
| \[5x+10y=70\] ...(iv) |
| On subtracting Eq. (i) from Eq. (iv), |
| we get |
| 7y=35 |
| \[\Rightarrow \,\,\,\,y=5\] |
| From Eq. (iii), we get |
| \[x+2\left( 5 \right)=14\] |
| 0\[\Rightarrow \,\,\,x+10=14\] |
| \[\Rightarrow \,\,x\,=4\] |
| So, \[\left( x,\,\,y \right)=\left( 4,\,\,5 \right)\] |
| [C] Given,\[15x+4y=61\] ...(i) |
| and \[4x+15y=72\] ...(ii) |
| On multiplying Eq. (i) by 4 and Eq. (ii) |
| by 15, we get |
| \[60x+16y=244\] ...(iii) |
| and \[60x+225y=1080\] ...(iv) |
| On subtracting Eq. (iii) from Eq. (iv), |
| we get |
| \[209y\text{ }=836\] |
| \[\Rightarrow \,\,\,\,\,y=4\] |
| From Eq. (i), we get |
| \[15x\text{ }+4\text{ }\left( 4 \right)\text{ }=61\] |
| \[\Rightarrow \,\,\,\,15x+16=61\] |
| \[\Rightarrow \,\,\,\,15x=45\] |
| \[\Rightarrow \,\,\,\,x=3\] |
| So, \[\left( x,y \right)=\left( 3,4 \right)\] |
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