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x + 9y = –13

2x + 3y = –11

1 answer

To solve the system of equations

  1. \( x + 9y = -13 \) (Equation 1)
  2. \( 2x + 3y = -11 \) (Equation 2)

we can use the substitution or elimination method. Here, we'll use the substitution method.

Step 1: Solve one equation for one variable

Let's solve Equation 1 for \( x \):

\[ x = -13 - 9y \]

Step 2: Substitute this expression in the other equation

Now, substitute \( x \) in Equation 2:

\[ 2(-13 - 9y) + 3y = -11 \]

Step 3: Simplify and solve for \( y \)

Now simplify the equation:

\[ -26 - 18y + 3y = -11 \] \[ -26 - 15y = -11 \]

Now, isolate \( y \):

\[ -15y = -11 + 26 \] \[ -15y = 15 \] \[ y = -1 \]

Step 4: Substitute \( y \) back to find \( x \)

Now substitute \( y = -1 \) back into the expression for \( x \):

\[ x = -13 - 9(-1) \] \[ x = -13 + 9 \] \[ x = -4 \]

Solution

The solution to the system of equations is

\[ x = -4 \quad \text{and} \quad y = -1. \]

Thus, the solution in ordered pair form is \( (-4, -1) \).