Solve the system by substitution.
minus, 5, x, minus, 2, y, equals, minus, 40
−5x−2y=
−40
y, equals, 2, x, plus, 2
y=
2x+2

We are given the following system of equations:

1. \(-5x - 2y = -40\)
2. \(y = 2x + 2\)

### Step 1: Substitute the expression for \(y\) from the second equation into the first equation.
Since \(y = 2x + 2\), substitute this into the first equation:

\[
-5x - 2(2x + 2) = -40
\]

### Step 2: Simplify the equation.
Distribute \(-2\) across \((2x + 2)\):

\[
-5x - 4x - 4 = -40
\]

Combine like terms:

\[
-9x - 4 = -40
\]

### Step 3: Solve for \(x\).
Add 4 to both sides:

\[
-9x = -36
\]

Divide by \(-9\):

\[
x = 4
\]

### Step 4: Substitute \(x = 4\) back into the second equation to find \(y\).
Use \(y = 2x + 2\) and substitute \(x = 4\):

\[
y = 2(4) + 2 = 8 + 2 = 10
\]

### Solution:
The solution to the system is \(x = 4\) and \(y = 10\).

### Final Answer:
\[
(x, y) = (4, 10)
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Solve the system: \(2x + y = 5\), \(y = 3x + 1\).
2. Solve the system: \(x + 2y = 6\), \(y = x - 3\).
3. Solve the system: \(3x - y = 9\), \(y = 4x - 7\).
4. Solve the system: \(5x + 3y = 15\), \(y = 2x + 5\).
5. Solve the system: \(4x - y = 12\), \(y = 5x - 3\).

**Tip:** Always double-check your substitution and arithmetic when solving systems by substitution!

Solve the system by substitution. −5x−2y=−40, y=2x+2

Learn how to solve the system of linear equations −5x−2y=−40 and y=2x+2 by substitution with step-by-step guidance. This problem covers essential algebraic concepts like substitution and solving for variables. Ideal for students in Grades 8-10.

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