Question

Line H is represented by the following equation: 2x + 2y = 8

What is most likely the equation for line K so the set of equations has infinitely many solutions?
x + 2y = 2
x + y = 4
2x + y = 6
x − y = 8

Answer 1

infinitely many solutions....you are gonna need to find a line that is the same for there to be infinite solutions. That means it has to have the same slope and the same y intercept. So you need to put everything in y = mx + b form and compare the slopes and the y intercepts.

Answer 2

2x + 2y = 8
2y = -2x + 8
y = -x + 4
In y = mx + b form, the slope is in the m position and the y intercept is in the b position.
So the slope is -1 and the y intercept is 4.
Now put your answer choices in y = mx + b form....your answer will have a slope of -1 and a y intercept of 4.
Any ideas now ?

Answer 3

or an easier way would be to reduce 2x + 2y = 8 by dividing every term by 2.....leaving you with what ?

Answer 4

so its the last one im pretty sure because you said to divide everyone by one. So it leaves me with the last one?

Answer 5

no...
2x/2 + 2y/2 = 8/2
x + y = 4
understand ? This equation, along with the one given, will result in infinite solutions

Answer 6

Haha i didnt want the answer i wanted to try and solve it myself... im a little slow in math :P but thank you for trying to help me :)

Answer 7

do you understand what I did ? Do you have any questions at all ?

Answer 8

Yes i kinda did im still a bit confused but i get the concept thank you :)