InterviewSolution
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InterviewSolution
| 1. |
Solve x and y 152x-378y =-74,-378x+152y=-604 |
| Answer» The given equations are{tex}152x - 378y = -74{/tex} ...(i){tex}-378x\xa0+ 152y = -604{/tex}. ... (ii)Clearly, the coefficients of x\xa0and y in one equation are interchanged in the other.Adding (i) and (ii), we get{tex}(152-378)x\xa0+ (-378 +152) y = -(74 + 604){/tex}{tex}\\Rightarrow{/tex}\xa0{tex}(-226)x\xa0+ (-226)y = -678{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}(-226)(x + y) = -678{/tex}{tex}\\Rightarrow \\quad ( x + y ) = \\frac { - 678 } { - 226 } \\Rightarrow x + y = 3{/tex}. ...(iii)Subtracting (ii) from (i), we get{tex}(152 + 378) x + (-378 - 152)y = (-74 + 604){/tex}{tex}\\Rightarrow{/tex}530x\xa0- 530y = 530{tex}\\Rightarrow{/tex}\xa0530(x - y) = 530 {tex}\\Rightarrow{/tex}\xa0x\xa0- y = 1. ... (iv)Adding (iii) and (iv), we get 2x = 4 {tex}\\Rightarrow{/tex}\xa0x = 2.Subtracting (iv) from (iii), we get2y = 2 {tex}\\Rightarrow{/tex} y = 1.Hence, x = 2 and y = 1 | |