To determine whether the ordered pair [tex]\((-5,6)\)[/tex] is a solution to the equation [tex]\(4x - y = -25\)[/tex], we need to substitute the values [tex]\(x = -5\)[/tex] and [tex]\(y = 6\)[/tex] into the equation and see if the equation holds true.
Step-by-Step Solution:
1. Substitute the value of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the equation [tex]\(4x - y = -25\)[/tex].
Given:
[tex]\[
x = -5, \quad y = 6
\][/tex]
The equation is:
[tex]\[
4x - y = -25
\][/tex]
2. Substitute [tex]\(x = -5\)[/tex] and [tex]\(y = 6\)[/tex] into the left-hand side of the equation:
[tex]\[
4(-5) - 6
\][/tex]
3. Calculate the left-hand side:
[tex]\[
4(-5) = -20
\][/tex]
[tex]\[
-20 - 6 = -26
\][/tex]
4. Now compare the result [tex]\( -26 \)[/tex] with the right-hand side of the equation:
[tex]\[
\text{Right-hand side:} \quad -25
\][/tex]
Since the left-hand side [tex]\((-26)\)[/tex] does not equal the right-hand side [tex]\((-25)\)[/tex], the equation [tex]\(4x - y = -25\)[/tex] is not satisfied.
Therefore, the correct choice is:
D. The ordered pair [tex]\((-5,6)\)[/tex] is not a solution to the equation because substituting the values from the ordered pair into the equation results in [tex]\(-26\)[/tex] instead of [tex]\(-25\)[/tex].
