Find x and y if \left[\begin{array}{cc}x & 3 x \ y & 4 y]\end{array}\left[\begin{array}{c}2 \ 1]\end{array}=\left[\begin{array}{c}5 \ 12]\end{array}

ICSE Class X Math 2013 Solved Paper - Question 32

Question : 32 of 46

Marks: +1, -0

Find

x

and

y

{[\table x , 3 x ; y , 4 y]}{[\table 2 ; 1]}={[\table 5 ; 12]}

Solution:

Given :

{{[\table x , 3 x ; y , 4 y ]}{[\table 2 ; 1 ]} }\;={[\table 5 ; 12 ]}

{{[\table 2 x+3 x ; 2 y+4 y ]} }\;={[\table 5 ; 12 ]}

{{[\table 5 x ; 6 y ]} }\;={[\table 5 ; 12 ]}

∴ 5 x\;=5

⇒ x\;=1

and

6 y\;=12

⇒ y\;=2

Hence,

x=1

and

y=2

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