Solve the system using substitution. 3 x plus 2 y equals 23. one-half x minus 4 equals y. (1 point) Responses the ordered pair (9, negative 2) Image with alt text: the ordered pair (9, negative 2) the ordered pair (27 over 4, negative 5 over 8) Image with alt text: the ordered pair (27 over 4, negative 5 over 8) the ordered pair (31 over 4, negative one-eighth) Image with alt text: the ordered pair (31 over 4, negative one-eighth) the ordered pair (three halves, negative 13 over four)
To solve the system using substitution, we first solve one of the equations for one variable and then substitute it into the other equation.
From the second equation, we can solve for y in terms of x:
\[y = \frac{1}{2}x - 4\]
Next, we substitute this expression for y into the first equation:
\[3x + 2\left(\frac{1}{2}x - 4\right) = 23\]
Simplifying, we get:
\[3x + x - 8 = 23\]
\[4x - 8 = 23\]
\[4x = 31\]
\[x = \frac{31}{4}\]
Now, we substitute this value of x into the second equation to find y:
\[y = \frac{1}{2}\left(\frac{31}{4}\right) - 4\]
\[y = \frac{31}{8} - 4\]
\[y = \frac{31}{8} - \frac{32}{8}\]
\[y = -\frac{1}{8}\]
Therefore, the solution to the system of equations is the ordered pair: \boxed{\left(\frac{31}{4}, -\frac{1}{8}\right)}