Solve the following system of equations by elimination method:8x + 5y

1.	Solve the following system of equations by elimination method:8x + 5y = 93x + 2y = 4
Answer» Given pair of linear equations is 8x + 5y = 9 …(i) And 3x + 2y = 4 …(ii) On multiplying Eq. (i) by 2 and Eq. (ii) by 5 to make the coefficients of y equal, we get the equation as 16x + 10y = 18 …(iii) 15x + 10y = 20 …(iv) On subtracting Eq. (iii) from Eq. (iv), we get 15x + 10y – 16x – 10y = 20 – 18 ⇒ – x = 2 ⇒ x = – 2 On putting x = – 2 in Eq. (ii), we get 3x + 2y = 4 ⇒ 3( – 2) + 2y = 4 ⇒ – 6 + 2y = 4 ⇒ 2y = 4 + 6 ⇒ 2y = 10 y = 10/2 = 5 Hence, x = 2 and y = 5 , which is the required solution.

Solve the following system of equations by elimination method:8x + 5y = 93x + 2y = 4

Answer»

Given pair of linear equations is

8x + 5y = 9 …(i)

And 3x + 2y = 4 …(ii)

On multiplying Eq. (i) by 2 and Eq. (ii) by 5 to make the coefficients of y equal, we get the equation as

16x + 10y = 18 …(iii)

15x + 10y = 20 …(iv)

On subtracting Eq. (iii) from Eq. (iv), we get

15x + 10y – 16x – 10y = 20 – 18

⇒ – x = 2

⇒ x = – 2

On putting x = – 2 in Eq. (ii), we get

3x + 2y = 4

⇒ 3( – 2) + 2y = 4

⇒ – 6 + 2y = 4

⇒ 2y = 4 + 6

⇒ 2y = 10

y = 10/2 = 5

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