Question

1. \

$$\begin{cases} -3b + a = 7 \\\\ 5a + 6b = 14 \\end{cases}$$

Explanation:

Step1: Eliminate $b$ via equation scaling

Multiply first equation by 2:
$2(-3b + a) = 2\times7$
$\implies -6b + 2a = 14$

Step2: Add to second equation

Add scaled equation to $5a+6b=14$:
$(-6b + 2a) + (5a + 6b) = 14 + 14$
$\implies 7a = 28$

Step3: Solve for $a$

Divide both sides by 7:
$a = \frac{28}{7} = 4$

Step4: Substitute $a=4$ to find $b$

Plug $a=4$ into $-3b + a = 7$:
$-3b + 4 = 7$
$\implies -3b = 7 - 4 = 3$
$\implies b = \frac{3}{-3} = -1$

Answer:

$a=4$, $b=-1$