Find the solution of the system of equations.

minus, x, plus, 9, y, equals, minus, 19

−*x*+9*y*=

−19

3, x, minus, 3, y, equals, 9

3*x*−3*y*=

9




Let's solve the system of linear equations:

\[
\begin{aligned}
-x + 9y & = -19 \quad \text{(Equation 1)} \\
3x - 3y & = 9 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 1: Solve one equation for \( x \) or \( y \)
Let's solve Equation 2 for \( x \):

\[
3x - 3y = 9
\]

Divide the entire equation by 3:

\[
x - y = 3
\]

Add \( y \) to both sides:

\[
x = y + 3 \quad \text{(Equation 3)}
\]

### Step 2: Substitute \( x = y + 3 \) into Equation 1
Substitute \( x = y + 3 \) into Equation 1:

\[
-(y + 3) + 9y = -19
\]

Simplify and solve for \( y \):

\[
-y - 3 + 9y = -19
\]

\[
8y - 3 = -19
\]

Add 3 to both sides:

\[
8y = -16
\]

Divide by 8:

\[
y = -2
\]

### Step 3: Substitute \( y = -2 \) back into Equation 3
Substitute \( y = -2 \) into Equation 3:

\[
x = -2 + 3 = 1
\]

### Solution
The solution to the system of equations is:

\[
x = 1, \quad y = -2
\]

Would you like a detailed explanation of any step, or do you have any questions?

Here are 5 related questions:

1. How do you solve a system of equations using the elimination method?
2. What are the different types of solutions a system of linear equations can have?
3. How do you graphically represent the solution of a system of equations?
4. What is the significance of the determinant in solving systems of equations?
5. How can systems of equations be applied in real-world problems?

**Tip:** When dealing with negative signs in equations, be careful with arithmetic to avoid mistakes.

Learn how to solve the system of equations -x + 9y = -19 and 3x - 3y = 9 with a detailed step-by-step solution. This problem covers linear equations and the substitution method. Suitable for high school students.

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