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:

$$
LATEXBLOCK0
$$

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:

\((-1.4, 1.5)\)