Question

which is the approximate solution for the system of equations $3x + 4y = 2$ and $4x + y = -4$?\
\\(\circ\\) $(-1.4, 1.5)$\
\\(\circ\\) $(1.4, 1.5)$\
\\(\circ\\) $(0.9, -0.2)$\
\\(\circ\\) $(-0.9, -0.2)$

Explanation:

Step1: Solve the system of equations

We have the system:
\[

$$\begin{cases} 3x + 4y = 2 \\ 4x + y = -4 \end{cases}$$

\]
From the second equation, solve for \(y\): \(y = -4 - 4x\)

Step2: Substitute \(y\) into the first equation

Substitute \(y = -4 - 4x\) into \(3x + 4y = 2\):
\[
3x + 4(-4 - 4x) = 2
\]
\[
3x - 16 - 16x = 2
\]
\[
-13x - 16 = 2
\]
\[
-13x = 18
\]
\[
x = -\frac{18}{13} \approx -1.4
\]

Step3: Find \(y\) using \(x\)

Substitute \(x \approx -1.4\) into \(y = -4 - 4x\):
\[
y = -4 - 4(-1.4)
\]
\[
y = -4 + 5.6
\]
\[
y = 1.6 \approx 1.5
\]

Answer:

\((-1.4, 1.5)\)