Question

solve the system of equations $x - y = -1$ and $x + 8y = 35$ by combining the equations.

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$$\begin{pmatrix}x & -y & = -1\\\\x & +8y & = 35\\end{pmatrix}$$

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$$\begin{align*}x & - y & = -1\\\\x & + 8y & = 35\\\\\\hline \\square x + & \\ \\ \\ y & = \\ \\ \\ \\square\\end{align*}$$

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Explanation:

Step1: Eliminate x via subtraction

Subtract the first equation from the second:
$$(x + 8y) - (x - y) = 35 - (-1)$$

Step2: Simplify to solve for y

$$x + 8y - x + y = 35 + 1$$
$$9y = 36$$
$$y = \frac{36}{9} = 4$$

Step3: Substitute y into first equation

Plug $y=4$ into $x - y = -1$:
$$x - 4 = -1$$

Step4: Solve for x

$$x = -1 + 4 = 3$$

Answer:

$x=3$, $y=4$

To fill the combination step:
Multiply the first equation by $-1$:
$$-1 \times (x - y = -1) \implies -x + y = 1$$
Add to the second equation:
$$(-x + y) + (x + 8y) = 1 + 35$$
$$0x + 9y = 36$$
So the blanks are: top box $-1$, bottom box $1$, final box $0$, right side $36$