Solve the system using substitution. Check your answer.
yequalsnegative 3xplus12
6yminusxplus4equals0

We are given the following system of equations:

1. \( y = -3x + 12 \)
2. \( 6y - x + 4 = 0 \)

### Step 1: Substitute the expression for \( y \) from Equation 1 into Equation 2.

From Equation 1, we know:
\[
y = -3x + 12
\]

Now substitute this into Equation 2:

\[
6(-3x + 12) - x + 4 = 0
\]

### Step 2: Simplify and solve for \( x \).

Expand the terms:
\[
6(-3x + 12) = -18x + 72
\]
Now substitute back:
\[
-18x + 72 - x + 4 = 0
\]
Combine like terms:
\[
-19x + 76 = 0
\]
Solve for \( x \):
\[
-19x = -76
\]
\[
x = 4
\]

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

Now that we have \( x = 4 \), substitute it back into Equation 1 to find \( y \):

\[
y = -3(4) + 12 = -12 + 12 = 0
\]

### Step 4: Check the solution.

Substitute \( x = 4 \) and \( y = 0 \) into the second equation:

\[
6(0) - 4 + 4 = 0
\]
\[
0 = 0
\]
Since the equation holds true, the solution is correct.

### Final Answer:
The solution to the system of equations is \( x = 4 \) and \( y = 0 \).

Would you like more details or have any questions?

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**Related Questions:**
1. How does the substitution method work in solving systems of equations?
2. What other methods can be used to solve systems of linear equations?
3. How do you solve a system of equations graphically?
4. What happens when the system of equations has no solution?
5. Can the substitution method be applied to non-linear systems?

**Tip:** Always substitute your solution back into both original equations to ensure your solution is correct!

Solve the system using substitution. Check your answer. y = -3x + 12, 6y - x + 4 = 0

Learn how to solve the system of equations y = -3x + 12 and 6y - x + 4 = 0 using the substitution method. This step-by-step guide covers key algebra concepts and is suitable for students in Grades 8-10.

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