Question

3x+2y=4 and 8x+5y=9 find the value of x and y​

Answer 1

Step-by-step explanation:

➜ In order to make the coefficients of x equal multiply the equation 8x + 5y = 9 by 3 and equation 3x + 2y = 4 by 3

${\bold{\sf{Then \: we \: get \: the \: equations:}}}$

${\bold{\sf{24 x \: + \: 15 y \: = \: 27 . . . ( 1 )}}}$

${\bold{\sf{24 x \: + \: 1 6 y \: = \: 32 . . . ( 2 )}}}$

➜Subtract Equation (1) from Equation (2) to eliminate x , because the coefficients of x are the same.

${\bold{\sf{So, \: we \: get \: ( 24 x − 24 x ) \: + \: ( 16 y − 15 y )}}}$

${\bold{\sf{= \: 32 \: − \: 27}}}$

${\bold{\sf{i.e. \: y \: = \: 5}}}$

➜Substituting this value of y in the equation 8x + 5y = 9 ,

${\bold{\sf{we \: get \: 8x + 25 \: = \: 9}}}$

${\bold{\sf{i.e. \: 8x \: = \: − 16}}}$

${\bold{\sf{i.e. \: x \: = \: −2}}}$

$\\ \\ {\large{\sf{\fbox{\red{Hence, the solution of the equations is x = − 2 , y = 5}}}}}$

Answer 2

Answer:

Multiply the equations by 8 and 3 respectively

24x+15y=27...(1)

24x+16y=32...(2)

➜Subtract Eq.(1) from Eq. (2) to eliminate x.

y=32−27

.y=5

➜Substituting this value of y in the equation 8x + 5y = 9 ,

8x+25=9

8x=−16

x=−2

Hence, the solution of the equations is x = − 2 , y = 5