Question

Select the statement that correctly describes the solution to this system of equations.-3x+2y=-22
-5=-4x+27

A.
There is no solution.

B.
There are infinitely many solutions.

C.
There is exactly one solution at
.

D.
There is exactly one solution at
.

Answer 1

To determine the correct statement about the system of equations given:

1. \(-3x + 2y = -22\)
2. \(-5 = -4x + 27\)

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).