Question

Solve the system by substitution.
a + b - 2c = 14
4b + c = -1
C = -5

Answer 1

(3, 1, - 5 )

Explanation:

a + b - 2c = 14 → (1)

4b + c = - 1 → (2)

c = - 5 → (3)

substitute c = - 5 into (2)

4b - 5 = - 1 ( add 5 to both sides )

4b = 4 ( divide both sides by 4 )

b = 1

substitute b = 1 and c = - 5 into (1)

a + 1 - 2(- 5) = 14

a + 1 + 10 = 14

a + 11 = 14 ( subtract 11 from both sides )

a = 3

solution is (3, 1, - 5 )

as a check substitute values into (1) and (2)

a + b + c = 3 + 1 - 2(- 5) = 4 + 10 = 14 ← correct

4b + c = 4(1) - 5 = 4 - 5 = - 1 ← correct

Answer 2

a = 3 ; b = 1 ; c = -5

Explanation:

Solving system of equations by substitution method:

a +b - 2c = 14 -----------------------------(I)

4b + c = -1 -----------------------------(II)

c = -5 ------------------(III)

Substitute c = -5 in equation (II) and find the value of 'b',

4b + (-5) = -1

4b = -1 + 5

4b = 4

b = 4 ÷ 4

`\sf \boxed{b = 1}`

Substitute c = -5 and b = 1 in equation (I)

a + 1 - 2*(-5) = 14

a + 1 + 10 = 14

a +11 = 14

a = 14 - 11

`\sf \boxed{a = 3 }`

Verification:

a + b - 2c = 14

LHS = a + b - 2c

= 3 + 1 - 2*(-5)

= 3 + 1 + 10

= 14 = RHS

Hence verified.