SOLUTION: Solve the following system by substitution. x=7y+24 x=(7/4)y My work: (7/4)y = 7y+24 multiply each side by 4 7y=28y+96 divide by 7 y= 4y+(96/7) move the Y and 96/7 t

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Question 619449: Solve the following system by substitution.
x=7y+24
x=(7/4)y
My work:
(7/4)y = 7y+24
multiply each side by 4
7y=28y+96
divide by 7
y= 4y+(96/7)
move the Y and 96/7 to the other side
-(96/7) = 3y
I've multiplied 7 on both sides and then divided -672 = 21y which equals to -32
then input the -32 like this
x=7(-32)+24
x=-200
but on the second equation it does not match
x=(7/4)(-32)
x=-56
and here are my choices:
A. The solution set is {( _, _)} (Type an ordered pair)
B. The system has dependent equations. The solution set is {x,y)| _____}
c. The system is inconsisten. The solution set is undefined.
Found 2 solutions by jim_thompson5910, ewatrrr:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
x=7y+24

(7/4)y=7y+24

7y=4*(7y+24)

7y=28y+96

7y-28y=96

-21y=96

y=96/(-21)

y = -32/7
-------------------------

x = 7y+24

x = 7(-32/7)+24

x = -32+24

x = -8

Answer:

A. The solution set is {( -8, -32/7)} (Type an ordered pair)

B. The system has dependent equations. The solution set is {(x,y)| _____}

c. The system is inconsistent. The solution set is undefined.

Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi,
x=7y+24
x=(7/4)y
My work:
(7/4)y = 7y+24
multiply each side by 4
7y=28y+96
divide by 7
y= 4y+(96/7)
move the Y and 96/7 to the other side
Yes! -(96/7) = 3y and y = -32/7 and x = (7/4)(-32/7) = -8
(-8, -32/7) Independent system, one solution
CHECKING our Answer***
-8 = 7(-32/7) + 24 = -8
A consistent system has at least one solution.
An inconsistent system has no solutions.
An independent system has exactly one solution. ****
Andependent system has infinitely many solutions.