Question

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find the solution of the system of equations.
$x - y = -3$
$-8x + y = 45$
answer attempt 1 out of 2
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submit answer

Explanation:

Step1: Add the two equations to eliminate \( y \)

The system of equations is:
\[

$$\begin{cases} x - y = -3 \\ -8x + y = 45 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((x - y)+(-8x + y)=-3 + 45\)
Simplify the left - hand side: \(x - y-8x + y=(x-8x)+(-y + y)=-7x\)
Simplify the right - hand side: \(-3 + 45 = 42\)
So we get the equation \(-7x=42\)

Step2: Solve for \( x \)

To solve for \( x \), divide both sides of the equation \(-7x = 42\) by \(-7\):
\(x=\frac{42}{-7}=-6\)

Step3: Substitute \( x=-6 \) into the first equation to solve for \( y \)

Substitute \( x = - 6\) into the equation \(x - y=-3\):
\(-6-y=-3\)
Add 6 to both sides of the equation: \(-y=-3 + 6\)
Simplify the right - hand side: \(-y = 3\)
Multiply both sides by \(-1\) to get \(y=-3\)

Answer:

\((-6,-3)\)