Algebra Points: Solve the system by graphing.?

Question

2x + y = 3
2x + y = –1

The choices are below:

a. Inconsistent

b. (1, 2)

c. (0, –3)

d. (–1, 4)

Best Answer gets 10 points!

Answer 1

First, let's solve for y for each equation.
It'll also be easier if you put it in slope-intercept form (y=mx+b).

a. 2x+y=3
y=3-2x
y=-2x+3
b. 2x+y=-1
y=-1-2x
y=-2x-1

Okay, so now you have:
y=-2x+3
y=-2x-1

Since both equations are equal to y, you can use substitution since the arguments are true.
-2x+3=-2x-1
Add 2x to both sides.
3=-1 That is not true.
Therefore, your answer is A. inconsistent.

However, you asked to solve this system of equations graphically.
I tried graphing this on the computer so please excuse me if it's too messy to understand.

http://i5.photobucket.com/albums/y190/mandALiEN/systemsofequations-1.jpg

From the graph I have drawn, you can see that these lines do not intersect. The point of intersection is your solution, but there is no intersection. These are parallel lines. You can also know that this system has no solution by looking at their slopes. m=-2 in both equations. If both equations have the same slope, you automatically will know that they are parallel lines with no solution.

I hope that helps. Good luck with all your other math problems!

Answer 2

First, you would want to solve for "y" for both equations, and do substitution. You should get...

y = 3 - 2x
y = -1 - 2x

Since you have the same slope (which is -2x) for both equations when you solved for "y", it would mean that both lines are parallel to each other when you graph them. Remember the rule that if both lines have the same slope, they are parallel to each other. Since both lines are parallel, they are going to never touch each other meaning they will never cross paths. In that case, the only reasonable answer would be "(a) Inconsistent"

Hope I helped!

Answer 3

Have you tried plugging (er, "substituting") the given values into the equations, to see which answer makes both equations true?

Oh, wait, don't bother -- no matter what values you pick for x & y, it's impossible to add 2x+y and get 3 one time and -1 another time. The system is clearly inconsistent. Heh heh.

Hope that helps!

Answer 4

the following you want to remedy for y & put in kind y=mx+b. the position m is volume in the front of x & b is the volume by using itself. once you remedy for both one among those adult men you get y=-x-13 & y=2x+8; because you want to remedy by using graphing. b is the position the line hits the y axis and m is slope ( slope is upward thrust over run so 2 is up 2 over a million) graph both strains and the point the position they hit will be answer.

Answer 5

If you graphed these equations you would get two parrallel lines (never cross) the other methods for solving give you no solutions as the others have said.

Answer 6

The answer is a. Inconsistent

Answer 7

It's been a while, but I would go with answer 'a'.

essentially what you have is 3 = -1