-y=x

9x-7y=-16
Solve by substitution

1 answer

To solve the system of equations using substitution, we start with the two equations:

  1. \(-y = x\)
  2. \(9x - 7y = -16\)

First, we will solve the first equation for \(y\): \[ y = -x \]

Next, we substitute this expression for \(y\) in the second equation: \[ 9x - 7(-x) = -16 \]

This simplifies to: \[ 9x + 7x = -16 \]

Combining like terms gives: \[ 16x = -16 \]

Now, we solve for \(x\): \[ x = \frac{-16}{16} = -1 \]

With \(x = -1\), we now substitute this value back into the equation \(y = -x\) to find \(y\): \[ y = -(-1) = 1 \]

Thus, the solution to the system of equations is: \[ (x, y) = (-1, 1) \]

The solution is: \[ \boxed{(-1, 1)} \]