Question

Elimination method and substitution method

3x+4y=6
4x-y=5​

Answer 1

By substitution method-

3x + 4y = 6. -(1)

3x + 4y = 6. -(1)4x - y = 5. -(2)

3x + 4y = 6. -(1)4x - y = 5. -(2)Modifying eq.(2)

3x + 4y = 6. -(1)4x - y = 5. -(2)Modifying eq.(2) 4x = 5+y

x = 5+y / 4

Putting the value of x in eq.(1)

3(5+y/4) + 4y = 6

15+3y / 4 + 4y = 6

$\frac{15 + 3y + 16y}{4} = 6$

15 + 19y = 24

19y = 24-15

19y = 5

y = 5/19

Putting the value of y in eq.(2)

$4x - \frac{5}{19} = 5$

$\frac{76x - 5}{19} = 5$

76x - 5 = 95

76x = 100

x = 100/76

x = 50/38

x = 25/19

By elimination method:-

Multiplying eq.(2) by 4

So equation 1 = 3x + 4y = 6

equation 2 = 4 (4x - y = 5)

16x - 4y = 20

By equation 1 & 2

3x + 4y = 6

16x - 4y = 20

_______________

19x = 26

x = 26/19

Putting the value of x in eq.(1)

$3 \frac{26}{19} + 4y = 6$

78/19 + 4y = 6

$\frac{78 + 76y}{19} = 6$

78 + 76y = 114

76y = 114-78

76y = 36

y = 36/76

y = 9/19