Question

use a graphing tool to solve the system. \

$$\begin{cases} 13x + 6y = -30 \\\\ x - 2y = -4 \\end{cases}$$

which ordered pair is the best estimate for the solution to the system? $(-2.5, 0.75)$ $(0.75, -3.25)$ $(-2.5, 0.25)$ $(-1.96, 1.75)$

Explanation:

Step1: Isolate $x$ from second equation

From $x - 2y = -4$, we get $x = 2y - 4$.

Step2: Substitute $x$ into first equation

Substitute $x=2y-4$ into $13x + 6y = -30$:
$$13(2y - 4) + 6y = -30$$
Expand and simplify:
$$26y - 52 + 6y = -30$$
$$32y - 52 = -30$$

Step3: Solve for $y$

$$32y = -30 + 52$$
$$32y = 22$$
$$y = \frac{22}{32} = 0.6875 \approx 0.75$$

Step4: Solve for $x$

Substitute $y=0.6875$ into $x=2y-4$:
$$x = 2(0.6875) - 4 = 1.375 - 4 = -2.625 \approx -2.5$$

Answer:

$(-2.5, 0.75)$