Point of intersection of inequalities

[frctl]

I have the following inequalities:
6x + 4y ≤ 108
x + y ≤ 24
x ≥ 0
y ≥ 0

the equations in slope intercept form
4y = -6x + 108
y = -2/3x + 27
and
y = -x + 24

find the point of intersection algebraically
-(2/3x + 27) + 24
-2/3x = 51
-8.5 <- is this correct?
(Still need to find y value, sub into which equation)

 

[pka]

I have the following inequalities:
6x + 4y ≤ 108
x + y ≤ 24
x ≥ 0
y ≥ 0

The system is equivalent to
\(6x+4y=108\\4x+4y=96\\2x=12\\x=6.\) So what \(y=~?\)

 

[LCKurtz]

I have the following inequalities:
6x + 4y ≤ 108
x + y ≤ 24
x ≥ 0
y ≥ 0

the equations in slope intercept form
4y = -6x + 108
y = -2/3x + 27
and
y = -x + 24

find the point of intersection algebraically
-(2/3x + 27) + 24
-2/3x = 51
-8.5 <- is this correct?
(Still need to find y value, sub into which equation)

It obviously isn't correct because you were given [MATH]x \ge 0,~y\ge 0[/MATH]. Check the step I have colored red.

 

[frctl]

@pka In this case,
6 + y = 24
y = 4
but point (4, 6) is not on the graph



@LCKurtz yes
It should be -6/4

 

[pka]

@pka In this case,
6 + y = 24
y = 4
but point (4, 6) is not on the graph
View attachment 17540


@LCKurtz yes
It should be -6/4

Look at the graph HERE

 

[frctl]

Ok thank you

 

[Steven G]

I have the following inequalities:
6x + 4y ≤ 108
x + y ≤ 24
x ≥ 0
y ≥ 0

the equations in slope intercept form
4y = -6x + 108 OK
y = -2/3x + 27 No
and
y = -x + 24 OK

find the point of intersection algebraically
-(2/3x + 27) + 24 There is no equation here!
-2/3x = 51 I'll agree that 27+24=51 but how is there now an equal sign and why is the 51 on the other side of the equal sign?
-8.5 <- is this correct? How can this be right? On the right hand side of the < sign is just - !!!
(Still need to find y value, sub into which equation)

See my comments above.

 

[Steven G]

@pka In this case,
6 + y = 24
y = 4
but point (4, 6) is not on the graph

6 + 4 = 24??? I always thought that 20 + 4 = 24. For the record it is 6 + 18 = 24. So y =18.
Another mistake you made is that even if x=6 and y=4 the point would be (6,4) as the 1st number should be the value for and the 2nd number is the value for y.

 

[frctl]

Ah yes the point of intersection is (6, 18)