Question

solve the following pair of linear equations by the substitution and cross-multiplication method. 8x+5y=9. 3x+2y=4​

Answer 1

${\fbox{\boxed {\huge{\mathbb{\red{ANSWER:-}}}}}}$

${\underline{\underline{\green{\rm{By \: Substituting \: Method : }}}}}$

$\rm \blue{8x+5y= 9}$

$\rm \blue{3x + 2y = 4}$

8x+5y = 9. equation ......(1)

3x + 2y= 4. equation .....(2)

From equation(1)

$\rm8x + 5y = 9 \\ \rm8x = 9 - 5y \\ \rm x = {\frac{9 - 5y}{8}}$

Putting the value of x in equation(2)

$\rm3x + 2y= 4. \\ \implies{\rm 3 (\frac{9 - 5y}{8} + 2y ) = 4} \\ \implies{\rm(\frac{3(9 - 5y)}{8} + 2y ) = 4} \\ \implies{\rm\frac{3(9 - 5y) + 8(2y)}{8} = 4} \\ \implies{\rm3(9 - 5y) + 8(2y) = 4 \times 8} \\ }\implies{\rm27 - 15y + 16y = 32} \\ \implies{\rm27 + y = 32 \\ \rm y = 27 - 32} \\ \boxed {\implies{\rm \: y = 5}}$

Putting y in equation (2)

$\rm3x +2y =4 \\ </p><p>\implies{ \rm3x +2(5)=4} \\ </p><p>\implies{\rm3x+10=4} \\ </p><p>\implies{\rm 3x=4-10} \\ </p><p>\implies{\rm3x=-6}\\ \implies{\rm \: x = \frac{ - 6}{3}} \\ \boxed{\implies {\rm \: x = - 2}}$

Therefore x = -2 and y = 5

is the solution of given linear pair of equations

______________________

${\underline{\underline{\green{\rm{By \: Cross \: Multiplication \: Method : }}}}}$

${\orange{\rm8x + 5y = 9}} \\ \orange{ \rm3x + 2y = 4}$

From cross multiplication

8x + 5y - 9=0

3x + 2y - 4=0

$\bold{\rm{For (x)}}$

$\implies \rm\frac{x}{5x( - 4) - 2x( - 9)} \\ \rm \implies \frac{x}{ - 20 + 18} \\ \rm \implies{\boxed{\frac{ x}{ - 2}}}$

$\bold{\rm{For( Y)}}$

$\implies \rm\frac{y}{ (- 9) \times 3(- 4) \times 8} \\ \rm \implies \frac{y}{ - 27 + 32} \\ \rm \implies{\boxed{\frac{ y}{ 5}}}$

$\bold{\rm{For(1)}}$

$\implies \rm\frac{1}{ 8 \times 2(- 3) \times 5} \\ \rm \implies \frac{1}{ - 16 - 15} \\ \rm \implies{\boxed{\frac{ 1}{ 1}}}$

Now,

$\rm \frac{x}{ - 2} = \frac{1}{1} \\ \rm \implies{x = - 2 \times 1 }\\ \rm \implies{x = - 2}</p><p>$

$</p><p> \rm \frac{y}{ 5} = \frac{1}{1} \\ \rm \implies{y = 5\times 1 }\\ \rm \implies{ y= 5}$

Hence, x = -2 and y = 5 is the solution.

${\boxed{\huge{\green{\mathcal{BeBrainly}}}}}</p><p>$

Answer 2

The above given answer correct refer that..