Help with algebra 1 please 10 points.?

Question

6. Is the system consistent or inconsistent? y = -1/2x - 1 and y = 3x + 3
Consistent
Inconsistent
Cannot be determined

7. The system, 6x - 4y = 5 and 9x - 6y = 5, is consistent.
True
False

Answer 1

Change them to slope-intercept form: 6x - 4y = 5.

Subtract 6x from each side.

-4y = -6x + 5

Divide each side by -4.

y = (-6)/(-4)x - 5/4

Simplify y = 3/2x - 5/4

Now the other equation: 9x - 6y = 5

Subtract 9x from each side.

- 6y = -9x + 5

Divide each side by -6.

y = (-9)/(-6)x -5/6

Simplify y = 3/2x -5/6

Now let's compare the SLOPES and the INTERCEPTS of y = 3/2x - 5/4 and y = 3/2x -5/6.

They have the SAME slope (3/2) so they are PARALLEL they have DIFFERENT y-intercepts (-5/4) and (-5/6) respectively. So that means the lines are parallel and do not overlap.

So, it is false.

Answer 2

y = -1/2x - 1 and y = 3x + 3

Now let's compare the SLOPES and the INTERCEPTS of y = -1/2x - 1 and y = 3x + 3

They have the DIFFERENT slope (-1/2) and 3 so they are PERPENDICULAR.

They have DIFFERENT y-intercepts -1 and 3 respectively.

So that means the lines are perpendicular and do not overlap.

So, it is inconsistent.

Comments

The system of equations are y = (-1/2)x - 1 and y = 3x + 3.

To find the value of x, substitute y = 3x + 3 in y = (-1/2)x - 1.

3x + 3 = (-1/2)x - 1

3x +(1/2)x = - 1 - 3

7x/2 = - 4

7x = - 8

⇒ x = - 8/7.

To find the value of y, substitute x = - 8/7 in y = 3x + 3.

y = 3(- 8/7) + 3

y = - 24/7 + 3

y = (- 24 + 21)/7

⇒ y = - 3/7.

The solution of the given system is (x, y) = (- 8/7, - 3/7).

The system of equations that has at least one solution is Consistent.

So, the given system is consistent.