Solve the system by substitution.

minus, 7, x, minus, 10, y, equals, 40

−7*x*−10*y*=

40

x, equals, minus, 2, y

*x*=

−2*y*

To solve the system of equations using substitution, we are given the following two equations:

1. \(-7x - 10y = 40\)
2. \(x = -2y\)

### Step 1: Substitute \(x = -2y\) into the first equation

Since \(x = -2y\), substitute this expression for \(x\) in the first equation.

\[
-7(-2y) - 10y = 40
\]

### Step 2: Simplify the equation

\[
14y - 10y = 40
\]

Combine like terms:

\[
4y = 40
\]

### Step 3: Solve for \(y\)

Now divide both sides by 4:

\[
y = \frac{40}{4} = 10
\]

### Step 4: Solve for \(x\)

Now that we know \(y = 10\), substitute this value back into the equation \(x = -2y\):

\[
x = -2(10) = -20
\]

### Solution

The solution to the system of equations is:

\[
x = -20, \quad y = 10
\]

Would you like more details or have any questions? Here are five related questions you might explore:

1. How can you check the solution of a system of equations?
2. What happens if you graph the system of equations on a coordinate plane?
3. Can a system of equations have no solution or infinitely many solutions? When does that happen?
4. How would the solution change if the second equation was \(x = 2y\) instead of \(x = -2y\)?
5. What are some other methods to solve systems of equations besides substitution?

**Tip:** When solving by substitution, always simplify equations as much as possible before substituting values for easier calculations.

Solve the system by substitution. −7x - 10y = 40, x = -2y

Learn how to solve the system of equations −7x - 10y = 40 and x = -2y using the substitution method. This detailed solution covers essential algebraic concepts such as substitution and simplifying linear equations. Suitable for students in Grades 8-10.

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