Question

1. considere este sistema de ecuaciones.

resolver el sistema de ecuaciones mediante sustitución.

1. la siguiente gráfica muestra un sistema de ecuaciones lineales.

$y = -\frac{5}{4}x + 3$
$y = -\frac{5}{4}x - 2$
elija una opción para cada espacio en blanco para responder las preguntas a continuación.

las dos líneas en el sistema de ecuaciones anterior tienen pendientes que son
a different
b the same
son y
puntos de corte que son
a must be different
b must be the same
c can be the same or different

las líneas en el gráfico
se intersecan,
a parallel
b not parallel
a eventually
b never

Explanation:

Step1: Note missing first equation

The first system is incomplete (only $9x - 2y = 26$ is shown; no second equation is visible). We solve the second system and answer its associated questions.

Step2: Analyze linear equations

The system is:
$$y = -\frac{5}{4}x + 3$$
$$y = -\frac{5}{4}x - 2$$
In slope-intercept form $y=mx+b$, $m$ is slope, $b$ is y-intercept. Both have $m=-\frac{5}{4}$, $b$ values are 3 and -2 (different).

Step3: Answer first multiple choice

Slopes of parallel lines are equal.

Step4: Answer second multiple choice

Y-intercepts are 3 and -2, so they are different.

Step5: Answer third multiple choice

Parallel lines never intersect.

Step6: Answer fourth multiple choice

Parallel lines never cross, so they never intersect.

Answer:

1. (Incomplete system: missing second equation for problem 1; cannot solve)

2.

• First blank: B. must be the same
• Second blank: A. different
• Third blank: A. parallel
• Fourth blank: B. never