Question

1. \

$$\begin{cases} y = -10x - 1 \\\\ -10x + y = -21 \\end{cases}$$

Explanation:

Step1: Substitute y into second equation

Substitute $y = -10x - 1$ into $-10x + y = -21$:
$$-10x + (-10x - 1) = -21$$

Step2: Simplify the equation

Combine like terms and isolate constants:
$$-20x - 1 = -21$$
$$-20x = -21 + 1$$
$$-20x = -20$$

Step3: Solve for x

Divide both sides by -20:
$$x = \frac{-20}{-20} = 1$$

Step4: Solve for y

Substitute $x=1$ into $y=-10x-1$:
$$y = -10(1) - 1 = -11$$

Step5: Verify the solution

Check if $x=1, y=-11$ satisfies the second equation:
$$-10(1) + (-11) = -10 -11 = -21$$
This matches the right-hand side of the second equation.

Answer:

$x=1$, $y=-11$