To determine whether the ordered pair [tex]\((-3, -6)\)[/tex] is a solution to the given system of equations, we need to check if it satisfies both of the equations:
1. [tex]\(-4x + y = 6\)[/tex]
2. [tex]\(5x - y = 21\)[/tex]
Step-by-Step Verification
Equation 1: [tex]\(-4x + y = 6\)[/tex]
1. Substitute [tex]\(x = -3\)[/tex] and [tex]\(y = -6\)[/tex] into the equation.
[tex]\[
-4(-3) + (-6) = 6
\][/tex]
2. Simplify the left-hand side:
[tex]\[
12 - 6 = 6
\][/tex]
3. Check if the left-hand side equals the right-hand side:
[tex]\[
6 = 6
\][/tex]
The first equation is satisfied by the ordered pair [tex]\((-3, -6)\)[/tex].
Equation 2: [tex]\(5x - y = 21\)[/tex]
1. Substitute [tex]\(x = -3\)[/tex] and [tex]\(y = -6\)[/tex] into the equation.
[tex]\[
5(-3) - (-6) = 21
\][/tex]
2. Simplify the left-hand side:
[tex]\[
-15 + 6 = -9
\][/tex]
3. Check if the left-hand side equals the right-hand side:
[tex]\[
-9 \neq 21
\][/tex]
The second equation is not satisfied by the ordered pair [tex]\((-3, -6)\)[/tex].
Conclusion:
Since the ordered pair [tex]\((-3, -6)\)[/tex] satisfies the first equation but does not satisfy the second equation, it is not a solution to the entire system of equations. Therefore, the statement is false.
