Math, asked by arm1223, 1 year ago

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

Answers

Answered by poonam05
28

Answer:

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Answered by silentlover45
24

Given:-

  • 8x + 5y = 9
  • 3x +2y = 4

To find:-

  • Solve the linear equations by substitution and cross multiplication methods.

Solutions:-

  • 8x + 5y = 9 ..........(i).
  • 3x +2y = 4 ...........(ii).

From equation (ii).

3x + 2y = 4

  • x = (4 - 2y)/3 .......(iii).

Substitution the value of in equation (ii), we get.

8x + 5y = 9

8[(4 - 2y)/3] + 5y = 9

32 - 16y + 15y = 27

-y = 27 - 32

-y = -5

y = 5

Putting the value of y in Eq (ii), we get.

=> 3x + 2y = 4

=> 3x + 2(5) = 4

=> 3x + 10 = 4

=> 3x = 4 - 10

=> 3x = -6

=> x = -6/3

=> x = -2

Hence, x = -2 and y = 5.

Again, by cross - multiplication methods.

  • 8x + 5y - 9 = 0 ..........(i).
  • 3x +2y - 4 = 0 ...........(ii).

\leadsto \: \: \frac{x}{{({5} \: \times \: {4})} \: - \: {({9} \: \times \: {-2})}} \: = \:  \frac{y}{{({-9} \: \times \: {3})} \: - \: {({-5} \: \times \: {8})}} \: = \: \frac{1}{{({8} \: \times \: {2})} \: - \: {({3} \: \times \: {5})}}

\leadsto \: \: \frac{x}{{-20} \: - \: {(18)}} \: = \: \frac{y}{{-27} \: + \: {32}} \: = \: \frac{1}{1}

\leadsto \: \: \frac{x}{-2} \: = \: \frac{y}{5} \: = \: \frac{1}{1}

\leadsto \: \: \frac{x}{-2} \: = \: {1} \: \: \: \: \: \: and \: \: \: \: \: \:  \frac{y}{5} \: = \: {1}

=> x = -2 and y = 5

Hence, x = -2 and y = 5.

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