Question

I need answers to 6a and 6b. This is for my homework :,)

Answer 1

The system of equations has 3 cases

1. y = ax + b, y = ax + c

Since the coefficient of x and y are the same, and the y-intercepts are different, then

The two lines are parallel

2. y = ax + b, y = dx + c

Since the 2 lines have different coefficients of x, then

The two lines are intersected

3. y = ax + b, y = ax + b

Since the two lines have equal coefficients of x and equal y-intercepted, then

The two lines are coincide (same line)

6. a)

Since the system of equations is

`\begin{gathered} y=2x+3 \\ y=12x-2 \end{gathered}`

The coefficients of x not equal

Then from case 2 above

The two lines are intersected

6.b

Since the system of equations is

`\begin{gathered} y=13x+2 \\ y=13x-2 \end{gathered}`

The coefficients of x are equal

The y-interceptes not equal

Then from case 1 above

The two lines are parallel