Question

Which system has no solutions?

Answer 1

A) x + y = -4
-3x + 2y = 2

B) x - 4y = -8
2x - 3y = -16

C) x - y = -2
3x - y = 0

D) x + y = -1
4x + 4y = -4

E) 4x + 6y = -12
2x + 3y = 9

& how do i determine whether it has no solution or not

Answer 2

Look for the system where both equations have the same slope but different intercepts. That will represent parallel lines that do not intersect and thus have no solution. A quick way to see parallel lines is when the coefficients of "x" and "y" are in the same ratio. That way, you don't have to convert to slope-intercept form to see that two lines have the same slope.

Answer 3

Extending that thought, 2 of the systems have lines where both are the slope. But only one of those 2 selections will have a different intercept.

Answer 4

"the slope" is supposed to be "the same slope"

Answer 5

If you aer not able to eyeball the equations to check for slope, then you have to convert all equations to the slope-intercept form

y = mx + b.

And then check the "m" values because "m" is your slope.

Answer 6

Which system has infinite solutions?
Which system has (1, 3) as the solution?
Which system has (-2, -2) as the solution?
Which system has (-8, 0) as the solution?

these are the questions for the rest of them..

Answer 7

so I need to put both equations in slope form?

Answer 8

That's slope-intercept form. You have to do that if you can't do it visually or in your head. After a while, you would be able to do these in your head at a glance. That comes with a little practice and just doing enough of these.

An infinity of solutions results from two equations written representing just one line. That means that one equation is a multiple of another.

at this point, I would suggest putting all equations in the point-slope form.

Answer 9

so let's say for a .. how would I put it in point-slope form? I know it's (y-y1)=m(x-x1)

Answer 10

You don't want point-slope form, you want slope-intercept form which is:

y = mx + b

It is called that because the right-hand side has "m" for slope and "b" for the y-intercept. The very first equation can be put into slope-intercept form by subtracting "x" from each side.

Answer 11

so the slope intercept form of a for both of the equations would be y = -x - 4 & y = 3/2x + 1 ?

Answer 12

yes, very good.

Answer 13

And since the system in "a" has equations of differing slopes, that system is intersecting lines and has one solution (one point), and that system is called "independent".

Answer 14

So what question would that answer?

Answer 15

Since we know that system ("a") has one solution, we can use either the elimination method or the substitution method to determine the point that satisfies both equations.

Answer 16

Since you put both equations in the slope-intercept form, you have 2 equations that have "y =" or just "y" on the left. So, just set both right-sides equal to each other and solve for "x". Once you get "x", take either equation and put that value of "x" into the equation and get "y".

Answer 17

x = -2

Answer 18

& y also is -2 right?

Answer 19

Okay, so basically i put the equations in slope int form, then solve for x and y. Thanks so much, you really did help :)