Question

Solve the following set of simultaneous equation.

3x - 5y = 16; x - 3y = 8

Answer 1

3x - 5y = 16   ...(1)

x - 3y = 8    ...(2)

From (2), x = 8 + 3y   ...(3)

substituting equation 3 in equation 1, we get

3(8 + 3y) − 5y = 16

24 + 9y − 5y = 16

9y − 5y = 16 − 24

4y = −8

y = `(− 8)/4`

y = −2

substituting y = −2 in equation 3, we get

x = 8 + 3y

x = 8 + 3 × (−2)

x = 8 − 6

x = 2

Therefore, x = 2 and y = −2.

Answer 2

3x − 5y = 16  ...(1)

x − 3y = 8     ...(2)

On multiplying both sides of equation (2) by 3,

3x − 9y = 24    ...(3)

Subtracting equation (1) from equation (3), we get

3x - 9y = 24    ...(3)
3x - 5y = 16    ...(1)
−      +     −  
− 4y  = 8

∴ 4y = −8

∴ y = `(- 8)/4`

∴ y = −2

Substituting y = −2 in equation (1), we get

∴ 3x − 5y = 16

∴ 3x − 5(−2) = 16

∴ 3x + 10 = 16

∴ 3x = 16 − 10

∴ 3x = 6 

∴ x = `6/3`

∴ x = 2