Question

Which statements about the system are true? Select two options. y = y equals StartFraction 1 over 3 EndFraction x minus 4.x – 4 3y – x = –7 The system has one solution. The system consists of parallel lines. Both lines have the same slope. Both lines have the same y–intercept. The equations represent the same line.

Answer 1

Answer:

The system consists of parallel lines ⇒ 2nd answer

Both lines have the same slope ⇒ 3rd answer

Step-by-step explanation:

Lets revise the types of the solutions of the system of equations

Case 1:

→ If the two equations have the same coefficients of the two variables

   and different numerical terms then the two equations represented

   by two parallel lines

Ex: ax + by = c , ax + by = d

Case 2:

→ If the two equations have the same coefficients of the two variables

   and same numerical term then the two equations represented

   by the same line

Ex: ax + by = c , ax + by = c

Case 3:

→ If the two equations have different coefficients of one of the variables

   or the two variables then they represented by two intersected lines

   and the system has one solution

Ex: ax + by = c , dx + ey = f

The system of equation is

* y = $\frac{1}{3}$ x - 4

* 3 y - x = -7

Multiply the first equation by 3

∴ 3 y = x - 12

Subtract both sides by x

∴ 3 y - x = - 12 ⇒ (1)

∵ 3 y - x = - 7 ⇒ (2)

The system of equations has same x-coefficient and same y-coefficient

in both equations but the numerical terms are different, then they

represented by two parallel lines as first case above

and parallel lines have the same slope

The system consists of parallel lines

Both lines have the same slope

Answer 2

Answer:

The y-intercept is -1

Step-by-step explanation:

The slope-intercept equation is y = 4 x minus 1.

The Point (3/8,1/2) corresponds to (x1, y1) in the point-slope form of the equation.