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]
