Question

3x+4y=5 and 5x-2y=9 elimination method step by step solving ​

Answer 1

Step-by-step explanation:

Given :-

3x+4y=5

5x-2y=9

To find :-

Solve the equations by Elimination method ?

Solution :-

Given pair of linear equations in two variables are 3x+4y=5 and 5x-2y=9

3x+4y = 5 ------------(1)

On multiplying it with 2

=> 6x+8y = 10 --------(2)

and

5x-2y=9 ---------------(3)

On multiplying it with 4

=> 20x-8y = 36 --------(4)

On adding (2)&(4) then

6x+8y = 10

20x-8y = 36

(+)

__________

26x +0 = 46

__________

26x = 46

=> x = 46/26

=> x = 23/13

On Substituting the value of x in (1) then

3(23/13)+4y = 5

=> (69/13)+4y = 5

=> 4y = 5-(69/13)

=> 4y = (65-69)/13

=> 4y = -4/13

=> y = -1/13

Therefore, x = 23/13 and y = -1/13

Answer:-

The solution for the given problem is

(23/13, -1/13)

Check:-

If x = 23/13 and y = -1/13 then

LHS of equation (1)

=> 3x+4y

=> (3/23/13)+4(-1/13)

=> (69/13)+(-4/13)

=> (69-4)/13

=> 65/13

=> 5

=> RHS

LHS = RHS is true

If x = 23/13 and y = -1/13 then

LHS of equation (2)

=> 5x-2y

=> 5(23/13)-2(-1/13)

=> (115/13)+(2/13)

=> (115+2)/13

=> 117/13

=> 9

=> RHS

LHS = RHS is true

Verified the given relations in the given problem.

Used Method:-

→ Elimination method

Answer 2

Answer:

The value of

$x \: is \: \frac{23}{13} \: and \: y \: is \: - \frac{1}{13} \: .$

Step-by-step explanation:

3x + 4y = 5 - (1)

5x - 2y = 9 - (2)

Multiplying 1 in equation (1) and 2 in equation (2) , we get

[3x+4y=5]×1

=> 3x + 4y = 5 -(3)

[5x-2y=9]×2

=> 10x - 4y = 18 -(4)

Adding equation (3) and (4) , we get

3x + 10x + 4y + (-4y) = 5 + 18

=> 13x = 23

$= > x = \frac{23}{13}$

Putting the value of x in equation (1) , we get

3x + 4y = 5

$= > (3 \times \frac{23}{13} ) + 4y = 5 \\ = > \frac{69}{13} + 4y = 5 \\ = > 4y = 5 - \frac{69}{13} \\ = > 4y = \frac{65 - 69}{13} \\ = > 4y = \frac{ - 4}{13} \\ = > y = - \frac{4}{13} \times \frac{1}{4} \\ = > y = - \frac{1}{13}$