what is the solution (a, b) to this system of linear equations?\n3a + 6b = 45\n2a - 2b = -12\n(-27, 6)\n(-1…

Explanation:

Step1: Multiply second equation

Multiply the equation $2a - 2b=-12$ by 3 to make the coefficient of $b$ opposite of that in the first - equation. $3\times(2a - 2b)=3\times(-12)$, which gives $6a-6b = - 36$.

Step2: Add the two equations

Add the new - equation $6a-6b=-36$ to the first equation $3a + 6b=45$. $(3a + 6b)+(6a-6b)=45+( - 36)$. Combining like terms: $3a+6a+6b - 6b=45 - 36$, so $9a=9$.

Step3: Solve for $a$

Divide both sides of $9a = 9$ by 9. $a=\frac{9}{9}=1$.

Step4: Substitute $a$ into an original equation

Substitute $a = 1$ into the equation $2a-2b=-12$. $2\times1-2b=-12$. $2-2b=-12$.

Step5: Solve for $b$

First, subtract 2 from both sides: $-2b=-12 - 2=-14$. Then divide both sides by - 2: $b=\frac{-14}{-2}=7$.

Answer:

C. $(1,7)$