2x + 3y = 8; 6x + 5y = 16. elimination method
Answers
EXPLANATION.
⇒ 2x + 3y = 8. - - - - - (1).
⇒ 6x + 5y = 16. - - - - - (2).
As we know that,
Multiply equation (1) by 5.
Multiply equation (2) by 3.
⇒ 2x + 3y = 8. - - - - - (1). x 5.
⇒ 6x + 5y = 16. - - - - - (2). x 3.
We write equation as,
⇒ 10x + 15y = 40. - - - - - (1).
⇒ 18x + 15y = 48. - - - - - (2).
Subtracting equation (1) and (2), we get.
⇒ 10x + 15y = 40. - - - - - (1).
⇒ 18x + 15y = 48. - - - - - (2).
⇒ - - -
We get,
⇒ - 8x = - 8.
⇒ x = 1.
Put the value of x = 1 in equation (1), we get.
⇒ 2x + 3y = 8.
⇒ 2(1) + 3y = 8.
⇒ 2 + 3y = 8.
⇒ 3y = 8 - 2.
⇒ 3y = 6.
⇒ y = 2.
Values of x = 1 and y = 2.
Solution :
Here, are given two equations which we've to solve by elimination method.
2x + 3y = 8 ...i)
6x + 5y = 16 ...ii)
Multiply i) by 6 and ii) by 2
(2x + 3y) × 6 = 8 × 6
=> 12x + 18y = 48 ...iii)
(6x + 5y) × 2 = 16 × 2
=> 12x + 10y = 32 ...iv)
Now, subtract iv) from iii)
=> (12x + 18y) - (12x + 10y) = 48 - 32
=> 12x + 18y - 12x - 10y = 16
=> 12x - 12x + 18y - 10y = 16
=> 18y - 10y = 16
=> 8y = 16
=> y = 2
Put the value of y in i)
=> 2x + 3y = 8
=> 2x + 3(2) = 8
=> 2x + 6 = 8
=> 2x = 8 - 6
=> 2x = 2
=> x = 1
Now, verify the results.
Again let's take i)
=> 2x + 3y = 8
=> 2(1) + 3(2) = 8
=> 2 + 6 = 8
=> 8 = 8
∴ x = 1 and y = 2.