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–x + 8y = 10

7x + 9y = –5

1 answer

To solve the system of equations:

  1. \(-x + 8y = 10\) (Equation 1)
  2. \(7x + 9y = -5\) (Equation 2)

We can use either the substitution method or the elimination method. Here, I'll use the elimination method.

First, let's multiply Equation 1 by 7 to help eliminate \(x\):

\[ 7(-x + 8y) = 7(10) \] \[ -7x + 56y = 70 \quad \text{(Equation 3)} \]

Now, we'll leave Equation 2 as it is and have:

  1. \(-7x + 56y = 70\)
  2. \(7x + 9y = -5\)

Now we can add Equation 3 and Equation 4:

\[ (-7x + 56y) + (7x + 9y) = 70 + (-5) \] \[ 0x + 65y = 65 \]

Now we can simplify: \[ 65y = 65 \] \[ y = 1 \]

Now that we have \(y\), we can substitute it back into Equation 1 to find \(x\):

\[ -x + 8(1) = 10 \] \[ -x + 8 = 10 \] \[ -x = 10 - 8 \] \[ -x = 2 \] \[ x = -2 \]

Thus, the solution to the system of equations is: \[ x = -2, \quad y = 1 \]

The solution can be written as the ordered pair \((-2, 1)\).