Solve the system by substitution.

minus, 2, x, plus, 7, y, equals, 15

−2*x*+7*y*=

15

6, y, equals, x

6*y*=

*x*

Let's solve the system of equations by substitution. The system you provided is:

1. \( -2x + 7y = 15 \)
2. \( 6y = x \)

### Step 1: Solve one equation for a variable
From the second equation, \( 6y = x \), we can express \( x \) in terms of \( y \):
\[
x = 6y
\]

### Step 2: Substitute this expression for \( x \) into the first equation
Now substitute \( x = 6y \) into the first equation \( -2x + 7y = 15 \):
\[
-2(6y) + 7y = 15
\]

### Step 3: Simplify and solve for \( y \)
Simplifying the equation:
\[
-12y + 7y = 15
\]
\[
-5y = 15
\]
\[
y = \frac{15}{-5} = -3
\]

### Step 4: Substitute \( y = -3 \) back into the equation \( x = 6y \)
Now substitute \( y = -3 \) into the equation \( x = 6y \):
\[
x = 6(-3) = -18
\]

### Final Answer:
The solution to the system of equations is:
\[
x = -18, \quad y = -3
\]

Would you like further clarification or details on this method?

Here are five related questions you might explore:
1. What is the substitution method in solving systems of equations?
2. How can you check if the solution to a system is correct?
3. When is the substitution method more convenient than the elimination method?
4. How can systems of equations be solved graphically?
5. Can systems of equations have no solution or infinitely many solutions?

**Tip:** Always substitute the values back into both original equations to verify your solution is correct.

Solve the system by substitution.

-2x + 7y = 15
6y = x

Learn how to solve a system of linear equations using the substitution method. The problem involves solving the system -2x + 7y = 15 and 6y = x with a step-by-step guide. This method is commonly used in algebra and is suitable for students in Grades 8-10.

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