Answered

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Determine if [tex]$(-2,1)$[/tex] is a solution to the following system of linear equations:

[tex]\[
\begin{array}{l}
6x - 3y = -15 \\
2x + y = -3
\end{array}
\][/tex]

A. True
B. False

Sagot :

GinnyAnswer
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
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