Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
x − 3y = −5
4x + 3y = 10

Answer 1

a) try to solve it if you get to one single solution x=something y=something_else then it is a single solution.
b) if you left with x=something*y+something_else that is infinite solutions
c) if you left with x=something and x=something_else - this is a contradiction thus - no solutions

Answer 2

i put no solotions the answer was wrong

Answer 3

with the first equation you solve for x subtracting it on both sides

Answer 4

This has unique solution x-3y=-5
4x+3y=10.
Multiplying first one by 4,
4x-12y=-20.
Subtracting from second.
15y=30,y=2. x=1

Answer 5

lets do (a) solve it
(from line 1) x - 3y = -5 thus x=3y-5
(from line 2) 4x + 3y = 10 thus 4(3y-5)+3y=10 thus 12y-20+3y=10 thus 15y=30 thus y = 2
back to x=3y-5 means x=3*2-5 x=1

Answer 6

giselle3214 you understand what i did?

Answer 7

ohkay so with this 2x − y = 5 and 3x+ y = −6
(first equation ) x = y-5
( second equation ) ??

Answer 8

line two confused me bratner

Answer 9

the idea is to start with one line as if it was the only one and solve for one of the unknowns. i solved for x. then go to the second line and substitute x with what you found from the first line
. you should be left with an equation with one unknown. solve it and you are through.

Answer 10

ohhhhhh you have to substitue for the second line i thought you solve for it again

Answer 11

here is example of "no solution" situation:
x+y=10
2x+2y=30
tell me if you can't calculate and make sure there is actually no solution.

Answer 12

i get it know then

Answer 13

thank you!

Answer 14

now*

Answer 15

it equals out to the same thing

Answer 16

i specifically "cooked" the equations to have no solution. please write your calculations so i can see what is wrong.

Answer 17

with the first one x and y equals to one so that would make the second one equals itself

Answer 18

no this is incorrect. concentrate on the first line and solve for x. tell me what you get.

Answer 19

the first line is x+y = 10

Answer 20

you minus x on both sides. y=x-10

Answer 21

actually you should get y=10-x

Answer 22

it matters the order?

Answer 23

the sign infront of the x and 10 matters because => 15 = 20-5 but not 15 = 5-20

Answer 24

see my point?

Answer 25

ohkay so it does. i see your point

Answer 26

no go to the second line and substitute y for 10-x ( we found that y = 10-x)
the second line was 2x+2y=30 .
you will be left with equation with one unknown (x) - solve it and tell me what you get.

Answer 27

2x+2(10-x)=30

Answer 28

good. now you can solve it for x.

Answer 29

2x=20-2x=30

Answer 30

x=10, x= -15

Answer 31

not really. 2x+2(10-x)=30 means that 2x+20-2x=30

Answer 32

i don't understand how the second "equals" sign got into one equation.

Answer 33

now you have 2x+20-2x=30 and that leads us to 20=30 (2x-2x is 0) which is not true ("contradiction"). which means that the set of equations that i gave you is absurd and has no solution.

Answer 34

im sooooo confsued

Answer 35

2x − y = 5
3x + y = −6

Answer 36

would that be one solution?

Answer 37

yes.

Answer 38

start with the first line and solve for say... y because it is multiplied only by (minus sign). what you get?

Answer 39

y=2x+5

Answer 40

that is wrong. 2x-y=5 / -2x from both sides /
you get -y=5-2x /multiply by -1 both sides
you get y=-5+2x / change order
you get y=+2x-5

Answer 41

-5?

Answer 42

yep . if you multiply 5 by -1 you get 5*(-1)=-5

Answer 43

i see you have trouble with multiplication by -1. it goes like this
-y = 5 - 2x /multiply by -1 both sides means
(-1)*(-y) = -1*(5-2x) /open paranthesis
y = -1*5-1*(-2x)
y = -5+2x
y = 2x - 5

Answer 44

the whole thing is to get rid of that minus sign that we get stuck with in front of y

Answer 45

now go to the second line and substitute that y with 2x-5

Answer 46

3x+y+-6
3x+y(2x-5)

Answer 47

its an equation it should have an equal sign. and by substituting i mean "write 2x-5 instead of y"

Answer 48

the idea is that we "already know what y is! y is 2x-5" that is how we get rid of all y in the second line.

Answer 49

try again?