Question

select the correct answer.
what is the value of b in this linear system?
a - b + c = -6
b - c = 5
2a - 2c = 4
a. -1
b. 1
c. 2
d. -3

Explanation:

Step1: Simplify third equation

Divide $2a - 2c = 4$ by 2:
$\frac{2a}{2} - \frac{2c}{2} = \frac{4}{2}$
$a - c = 2$
Rearrange to get $a = c + 2$

Step2: Substitute $a$ into first equation

Substitute $a = c + 2$ into $a - b + c = -6$:
$(c + 2) - b + c = -6$
Combine like terms:
$2c - b + 2 = -6$
Rearrange:
$2c - b = -8$

Step3: Isolate $c$ from second equation

From $b - c = 5$, rearrange to get $c = b - 5$

Step4: Substitute $c$ into new equation

Substitute $c = b - 5$ into $2c - b = -8$:
$2(b - 5) - b = -8$
Expand and simplify:
$2b - 10 - b = -8$
$b - 10 = -8$

Step5: Solve for $b$

Add 10 to both sides:
$b = -8 + 10$
$b = 2$

Answer:

C. 2