To determine the correct statement about the system of equations given:
- \(-3x + 2y = -22\)
- \(-5 = -4x + 27\)
Let's first rearrange the second equation:
\(-5 = -4x + 27\)
Rearranging gives:
\(-4x = -5 - 27\)
\(-4x = -32\)
Dividing by -4:
\(x = 8\)
Now that we have \(x = 8\), we will plug this value into the first equation to solve for \(y\):
Substituting \(x = 8\) into \(-3x + 2y = -22\):
\(-3(8) + 2y = -22\)
\(-24 + 2y = -22\)
Adding 24 to both sides:
\(2y = 2\)
Dividing by 2:
\(y = 1\)
So we found a unique solution: \(x = 8\) and \(y = 1\) or the coordinate point \((8, 1)\).
Thus, the correct description of the solution to this system of equations is:
C. There is exactly one solution at (8, 1).