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Which of the following is the solution of the system:

[tex]\[
\left\{
\begin{aligned}
4x - y & = -1 \\
-4x - y & = 7
\end{aligned}
\right.
\][/tex]

Select the correct answer below:
A. [tex]$(-2, -7)$[/tex]
B. [tex]$(0, -7)$[/tex]
C. [tex]$(0, 1)$[/tex]
D. [tex]$(-1, -3)$[/tex]



Answer :

GinnyAnswer
To solve the system of equations

[tex]\[ \left\{\begin{aligned} 4x - y &= -1 \\ -4x - y &= 7 \end{aligned}\right. \][/tex]

we will follow a step-by-step algebraic method to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

1. Write down the two equations:

[tex]\[ 4x - y = -1 \quad \text{(Equation 1)} \][/tex]

[tex]\[ -4x - y = 7 \quad \text{(Equation 2)} \][/tex]

2. Add the two equations together to eliminate [tex]\( x \)[/tex]:

[tex]\[ (4x - y) + (-4x - y) = -1 + 7 \][/tex]

[tex]\[ 4x - y - 4x - y = 6 \][/tex]

[tex]\[ -2y = 6 \][/tex]

3. Solve for [tex]\( y \)[/tex]:

[tex]\[ y = -3 \][/tex]

4. Substitute [tex]\( y = -3 \)[/tex] back into one of the original equations to solve for [tex]\( x \)[/tex]. We can use Equation 1:

[tex]\[ 4x - y = -1 \][/tex]

[tex]\[ 4x - (-3) = -1 \][/tex]

[tex]\[ 4x + 3 = -1 \][/tex]

[tex]\[ 4x = -1 - 3 \][/tex]

[tex]\[ 4x = -4 \][/tex]

[tex]\[ x = -1 \][/tex]

So the solution to the system of equations is [tex]\( (-1, -3) \)[/tex].

Therefore, the correct answer is:

[tex]\[ (-1, -3) \][/tex]

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