Solve the system by substitution.
y, equals, minus, 8, x, minus, 49
y=
−8x−49
y, equals, minus, x
y=
−x


We are given a system of two equations:

\[
y = -8x - 49
\]
\[
y = -x
\]

We will solve this system using the **substitution method**. Since both equations are already solved for \( y \), we can set the right-hand sides of the two equations equal to each other:

\[
-8x - 49 = -x
\]

Now, solve for \( x \):

1. Add \( 8x \) to both sides:

\[
-49 = 7x
\]

2. Divide both sides by 7:

\[
x = -7
\]

Now that we have \( x = -7 \), substitute this value back into one of the original equations to find \( y \). Let's use the equation \( y = -x \):

\[
y = -(-7) = 7
\]

Thus, the solution to the system is:

\[
x = -7, \quad y = 7
\]

Would you like further details or have any questions?

### Related questions:
1. How can you verify that this solution is correct?
2. What happens if you substitute the values into the other equation?
3. Can substitution be used for systems with three variables?
4. How does substitution compare to elimination in solving systems?
5. What kind of systems are best suited for substitution?

### Tip:
When using substitution, always check your solution by plugging it back into both original equations.

Solve the system by substitution.
y = -8x - 49
y = -x

Learn how to solve the system of equations y = -8x - 49 and y = -x using the substitution method. This problem demonstrates key algebraic concepts in linear systems, suitable for students in Grades 8-10. The solution shows step-by-step how to find x = -7 and y = 7.

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