Question

(+7x + -6y = +1)
-7x - 3y = -10

Explanation:

Step1: Write the system clearly

$$\begin{cases} 7x - 6y = 1 \\ -7x - 3y = -10 \end{cases}$$

Step2: Add the two equations

Add to eliminate $x$:
$$(7x - 6y) + (-7x - 3y) = 1 + (-10)$$
$$-9y = -9$$

Step3: Solve for $y$

Divide both sides by $-9$:
$$y = \frac{-9}{-9} = 1$$

Step4: Substitute $y=1$ into first equation

$$7x - 6(1) = 1$$
$$7x - 6 = 1$$

Step5: Solve for $x$

Add 6 to both sides, then divide by 7:
$$7x = 1 + 6 = 7$$
$$x = \frac{7}{7} = 1$$

Answer:

$x=1$, $y=1$