To solve the system of equations by substitution, we will follow these steps:
The two equations are:
- \(-2y = x\) (Equation 1)
- \(7x + 9y = -45\) (Equation 2)
Step 1: Solve Equation 1 for \(x\)
From Equation 1, we can express \(x\) in terms of \(y\): \[ x = -2y \]
Step 2: Substitute \(x\) in Equation 2
Now, substitute \(x = -2y\) into Equation 2: \[ 7(-2y) + 9y = -45 \]
Step 3: Simplify and solve for \(y\)
Simplifying this equation: \[ -14y + 9y = -45 \] \[ -5y = -45 \]
Now, divide both sides by -5: \[ y = \frac{-45}{-5} = 9 \]
Step 4: Substitute back to find \(x\)
Now, substitute \(y = 9\) back into the equation for \(x\): \[ x = -2(9) = -18 \]
Final Solution:
The solution to the system of equations is: \[ x = -18, \quad y = 9 \]
We can write it as an ordered pair: \[ (-18, 9) \]