Question

Solve the elimination method

7a + 6b = 3
-7a +b = 25

The solution of the system is?

Answer 1

7a + 6b = 3
-7a + b = 25

b = 7a + 25

Solve for a
7a + 6(7a + 25) = 3
7a + 42a + 150 = 3
49a + 150 = 3
49a = -147
a = -3

Solve for b
-7(-3) + b = 25
21 + b = 25
b = 4

Check answers
7a + 6b = 3
7(-3) + 6(4) = 3
-21 + 24 = 3

-7a + b = 25
-7(-3) + 4 = 25
-21 + 4 = 25

Answers:
a = -3
b = 4

Answer 2

7 a + 6 b = 3

+

-7 a + b = 25
________________

7 a + ( - 7 a ) + 6 b + b = 3 + 25

7 b = 28 Divide both sides by 7

7 b / 7 = 28 / 7

b = 4


7 a + 6 b = 3

7 a + 6 * 4 = 3

7 a + 24 = 3 Subtract 24 to both sides

7 a + 24 - 24 = 3 - 24

7 a = - 21 Divide both sides by 7

7 a / 7 = - 21 / 7

a = - 3


Proof :

-7 a + b = 25

- 7 * ( - 3 ) + 4 = 25

21 + 4 = 25