The first equation, 8x - 9y = - 23
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = ( 
, 3) and (x₂, y₂ ) = (- 4, - 1 )
m = 
= (- 4)/- 
= 
partial equation is y = x + c
to find c substitute either of the 2 points into the partial equation
using (- 4, - 1 ), then
- 1 = - 
+ c ⇒ c = 
y = x + ← in slope- intercept form
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
rearrange the slope- intercept equation into this form
multiply through by 9
9y = 8x + 23 ( subtract 9y and 23 from both sides )
8x - 9y = - 23 in standard form
Answer:
They would never intersect because they are parallel lines. You can tell they are parallel lines because they have the same slope and they have a different y-intercept. However, this doesn't mean that there was no solutions, there were, thats how i was able to tell what their slopes and y-intercepts were. So if there is an answer that you can choose from that explains that they won't intersect because they are parallel then that is the correct answer. It may be C, but I would see if there is another option.
Answer:
no solution
Step-by-step explanation:
-9x +5 < 17 AND 13x + 25 < -1
Solve each part separately and then put back together
-9x +5 < 17
Subtract 5 from each side
-9x+5-5< 17-5
-9x < 12
Divide each side by -9 remembering to flip the inequality
-9x/-9>12/-9
x > -4/3
and
13x + 25 < -1
subtract 25 from each side
13x +25-25 < -1-25
13x <-26
Divide by 13
13x/13 < -26/13
x <-2
There is no overlap so there is no solution
