Solve the system.

[tex]\[
\begin{array}{l}
y = -3x \\
x + y = 4
\end{array}
\][/tex]

A. [tex]\((-2, 6)\)[/tex]
B. [tex]\((-4, 12)\)[/tex]
C. [tex]\((-1, 3)\)[/tex]
D. [tex]\((1, -3)\)[/tex]



Answer :

To solve the given system of equations:
[tex]\[ \begin{array}{l} y = -3x \\ x + y = 4 \end{array} \][/tex]

we can use the substitution method. Here's a detailed step-by-step solution:

1. Substitute [tex]\( y \)[/tex] from the first equation into the second equation.
[tex]\[ y = -3x \rightarrow \text{Substitute this into} \ x + y = 4 \][/tex]

Therefore, we substitute [tex]\( y = -3x \)[/tex] into the equation [tex]\( x + y = 4 \)[/tex]:
[tex]\[ x + (-3x) = 4 \][/tex]

2. Simplify the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ x - 3x = 4 \][/tex]
[tex]\[ -2x = 4 \][/tex]

3. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{4}{-2} \][/tex]
[tex]\[ x = -2 \][/tex]

4. Substitute [tex]\( x = -2 \)[/tex] back into the first equation to find [tex]\( y \)[/tex]:
[tex]\[ y = -3x \][/tex]
[tex]\[ y = -3(-2) \][/tex]
[tex]\[ y = 6 \][/tex]

Thus, the solution to the system of equations is [tex]\( (x, y) = (-2, 6) \)[/tex].

So, the correct answer is:
a. [tex]\((-2, 6)\)[/tex]