Question

what is the solution (a, b) to this system of linear equations?
3a+6b=45
2a-2b=-12
○ (-27,6)
○ (-1, 7)
○ (1, 7)
○ (27, -6)

Explanation:

Step1: Simplify the second equation

Divide $2a-2b=-12$ by 2:
$a - b = -6$
Rearrange to isolate $a$:
$a = b - 6$

Step2: Substitute $a$ into first equation

Substitute $a = b - 6$ into $3a+6b=45$:
$3(b - 6) + 6b = 45$
Expand and simplify:
$3b - 18 + 6b = 45$
$9b - 18 = 45$

Step3: Solve for $b$

Add 18 to both sides:
$9b = 45 + 18 = 63$
Divide by 9:
$b = \frac{63}{9} = 7$

Step4: Solve for $a$

Substitute $b=7$ into $a = b - 6$:
$a = 7 - 6 = 1$

Answer:

C. (1, 7)