Intersection of the first two lines:

Multiply the first equation by 4 and the second by 5:

Subtract the two equations:

Plug this value for y in one of the equation, for example the first:

So, the first point of intersection is 
We can find the intersection of the other two lines in the same way: we start with

Use the fact that x and y are the same to rewrite the second equation as

And since x and y are the same, the second point is 
So, we're looking for a line passing through
and
. We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be 
In the attached figure, line
is light green, line
is dark green, and their intersection is point A.
Simiarly, line
is red, line
is orange, and their intersection is B.
As you can see, the line connecting A and B is the red line itself.
Answer:
- a) 2x -y = -5; A=2, B=-1, C=-5
- b) y = 2x +5
Step-by-step explanation:
a) Standard Form is ...
Ax + By = C
where A > 0 and A, B, C are mutually prime.
To get that form, we can add 2x-5 to both sides of the equation:
(2x -5) -2x = (2x -5) -y +5
-5 = 2x -y
Then we can swap sides of the equal sign:
2x -y = -5 . . . . . . standard form
Matching this to the generic standard form equation, we find ...
A = 2
B = -1
C = -5
__
b) We can solve for y by adding 2x+y to both sides of the equation:
(2x +y) -2x = (2x +y) -y +5
y = 2x +5 . . . . . . slope-intercept form
Answer:
The x-coordinates are translated 6 units to the left or right while the y-coordinates are not affected.
Step-by-step explanation:
The given triangle has vertices at A(-4,1), B(-2,1) and C(-2,4)
The transformation rule for a horizontal translation by k units is

In this case we have k=6



Therefore the x-coordinates are translated 6 units to the left or right while the y-coordinates are not affected.
See attachment
Answer:
<h2>y = |x - 5.5|</h2>
Step-by-step explanation:
y = f(x) + n - moves the graph n units up
y = f(x) - n - moves the graph n units down
y = f(x + n) - moves the graph n units to the left
y = f(x - n) - moves the graph n units to the right
===================================================
5.5 units to the right
y = f(x - 5.5) = |x - 5.5|