ICSE Class 10 Answered

Find L and M if 2L+3M =_{$begin mathsize 12px style open square brackets table row 9 22 row cell negative 11 end cell 1 end table close square brackets end style$}and 3L+4M=_{$begin mathsize 12px style open square brackets table row 12 31 row cell negative 14 end cell 1 end table close square brackets end style$}

Asked by Topperlearning User | 21 Sep, 2017, 10:59: AM

Expert Answer

Let 2L+3M = _{$begin mathsize 12px style open square brackets table row 9 22 row cell negative 11 end cell 1 end table close square brackets end style$}----equation 1

and 3L+4M=_{$begin mathsize 12px style open square brackets table row 12 31 row cell negative 14 end cell 1 end table close square brackets end style$}-----equation 2

Multiplying equation 1 with 3 on both sides, we get

6L+9M=_{$begin mathsize 12px style open square brackets table row 27 66 row cell negative 33 end cell 3 end table close square brackets end style$}------equation 3

Multiplying equation 2 with 2 on both sides, we get

6L+8M=_{$begin mathsize 12px style open square brackets table row 24 62 row cell negative 28 end cell 2 end table close square brackets end style$}------equation 4

Subtracting equation 4 from equation 3, we get

6L+9M -(6L+8M)= _{$begin mathsize 12px style open square brackets table row 27 66 row cell negative 33 end cell 3 end table close square brackets space minus space open square brackets table row 24 62 row cell negative 28 space end cell 2 end table close square brackets end style$}

Putting the value of M in equation 1, we get

2L+_{$begin mathsize 12px style open square brackets table row 9 12 row cell negative 15 end cell 3 end table close square brackets end style$}= _{$begin mathsize 12px style open square brackets table row 9 22 row cell negative 11 end cell 1 end table close square brackets end style$}