Question

An equation is shown below.

2x + y = 3

Part A: Explain how you will show all of the solutions that satisfy this equation. (4 points)

Part B: Determine three different solutions for this equation. (4 points)

Part C: Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent. (2 points) HELP PLEASE

Answer 1

@Lena772 @SolomonZelman @mathmale @undeadknight26 @seventhgradealgebra @oleg3321

Answer 2

@gswag98

Answer 3

@thecatmike

Answer 4

@jamieyang08

Answer 5

FOR PART A: 1 solution would be like subtracting "2x" from both sides

Answer 6

so then its y =3-2x?

Answer 7

no like this y = -2x + 3

Answer 8

O ok so then I need more solutions right?

Answer 9

another solution would be like y being part or unknown of in another equation

Answer 10

like what ?

Answer 11

like maybe 2x + 2y = 40 or something

Answer 12

?

Answer 13

and then you plug in what "y" equals then solve

Answer 14

ok hold on

Answer 15

soo @gswag98 whats b now I need 3 different parts?

Answer 16

well you can use the two that i gave you for Part A maybe

Answer 17

do i plug in for x and y

Answer 18

whatcha mean??

Answer 19

can i plug something in for x and y @gswag98

Answer 20

@phi

Answer 21

Part A: Explain how you will show all of the solutions that satisfy this equation. (4 points)

the answer could be: "plot the line defined by this equation. All points on the line are (x,y) pairs which are solutions to the equation"

Answer 22

So its not asking me for a equation.?

Answer 23

to plot the line, you can change from standard form to slope-intercept form
(but you don't have to)

However, to find 3 points on the line, it's helpful to rewrite the equation as
y = -2x+3

(btw you could write y= 3-2x, but it's convention to write the "x" part first)

Answer 24

to find 3 points, pick "nice numbers" for x, replace the x with that number, and find y

Answer 25

what do you mean nice numbers

Answer 26

easy to do the arithmetic. example: x=0 is easy to do. 3.14159 is not so easy

Answer 27

Oh yea haha

Answer 28

so i will plug in 2

Answer 29

an it =-1

Answer 30

that means when x=2, y = -1

(2,-1) is a point on the line, and a "solution"

if you use x=2 and y=-1 in the original equation, you will see it "works"

Answer 31

O yesssss hold on let me write this down

Answer 32

Ok so I have to make 2 more of those right?

Answer 33

yes. what did you come up with?

Answer 34

I came up with 3 and 5 i will do

Answer 35

i meant -5

Answer 36

I dont understand the last part @phi

Answer 37

First, what points did you get for part B?

Answer 38

For part C, they want you to write another equation to form
a system of equations

a system of equations means the solution must work for *both* equations at the same time.

Because your equations are lines, it means the solution must be on *both lines*.
That only happens where the lines cross. At the intersection point, that point is on both lines.

Answer 39

so they have to intersect like?

Answer 40

system of equations that is inconsistent
INCONSISTENT means no solution
no solution means the lines never cross.

lines that never cross are PARALLEL
so you need to find the equation of a line parallel to the original. Can you do that ?

Answer 41

yes I understand

Answer 42

-2x-3

Answer 43

Thank you for your help!!!!!

Answer 44

if you put y= in front of it

Answer 45

yess