what is the solution (a, c) to this system of linear equations? 2a - 3c = -6 a + 2c = 11 o (-\\frac{76}{7}…

Explanation:

Step1: Isolate $a$ in the second - equation

From $a + 2c=11$, we get $a = 11 - 2c$.

Step2: Substitute $a$ into the first equation

Substitute $a = 11 - 2c$ into $2a-3c=-6$. Then $2(11 - 2c)-3c=-6$. Expand the left - hand side: $22-4c-3c=-6$. Combine like terms: $22-(4c + 3c)=-6$, so $22 - 7c=-6$.

Step3: Solve for $c$

Subtract 22 from both sides: $-7c=-6 - 22=-28$. Divide both sides by $-7$: $c=\frac{-28}{-7}=4$.

Step4: Solve for $a$

Substitute $c = 4$ into $a = 11 - 2c$. Then $a=11-2\times4=11 - 8 = 3$.

Answer:

C. $(3,4)$