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Determine whether the ordered pair [tex]\((-5,6)\)[/tex] is a solution to the equation [tex]\(4x - y = -25\)[/tex].

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. 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 a false statement.

B. The ordered pair [tex]\((-5,6)\)[/tex] is a solution to the equation because substituting the values from the ordered pair into the equation results in a true statement.

C. The ordered pair [tex]\((-5,6)\)[/tex] is a solution to the equation because substituting the values from the ordered pair into the equation results in a true statement.

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 a false statement.



Answer :

GinnyAnswer
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].

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