To determine whether [tex]\((-2, 1)\)[/tex] is a solution to the given system of linear equations, we need to substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 1\)[/tex] into each equation and verify if they both hold true.
### Step 1: Check the first equation [tex]\(6x - 3y = -15\)[/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 1\)[/tex]:
[tex]\[
6(-2) - 3(1) = -12 - 3 = -15
\][/tex]
The left-hand side equals [tex]\(-15\)[/tex], which matches the right-hand side. Therefore, the first equation is satisfied.
### Step 2: Check the second equation [tex]\(2x + y = -3\)[/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 1\)[/tex]:
[tex]\[
2(-2) + 1 = -4 + 1 = -3
\][/tex]
The left-hand side equals [tex]\(-3\)[/tex], which matches the right-hand side. Therefore, the second equation is also satisfied.
### Conclusion
Since both equations are satisfied when [tex]\(x = -2\)[/tex] and [tex]\(y = 1\)[/tex], the point [tex]\((-2, 1)\)[/tex] is indeed a solution to the system of linear equations.
Therefore, the statement [tex]\((-2, 1)\)[/tex] is a solution to the given system of linear equations is:
True
