Question

-2y=x
7x+9y=-45
Solve by substitution

Answer 1

To solve the system of equations by substitution, we will follow these steps:

The two equations are:

1. \(-2y = x\) (Equation 1)
2. \(7x + 9y = -45\) (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:
\[
(-18, 9)
\]