Which system of equations below has infinitely many solutions? y = –3x + 4 and y = –3x – 4 y = –3x + 4 and 3y = –9x + 12 y = –3x + 4 and y = Negative one-thirdx + 4 y = –3x + 4 and y = –6x + 8

y = – 3x + 4 and 3y = – 9x + 12, y = –3x + 4 and y = –6x + 8

Step-by-step explanation:

Consider all Options as to solve this problem;

Option A; Here we are given equations y = – 3x + 4 and y = – 3x – 4. A system of equations can only have infinitely many solutions if the two equations are one in the same, such that their graphical representation overlap one another. Now the difference between the two equations is that the second has a y - intercept of - 4, rather 4 such that they are not one in the same equation.

Option B; We are given the following equations; y = – 3x + 4 and 3y = – 9x + 12. Convert the second equation to point - slope form, so that they can easily be compared, by dividing the second equation by 3: 3y = –9x + 12 ⇒ y = - 3x + 4. y = - 3x + 4, and y = - 3x + 4 are one in the same equation, thus this system of equations has infinitely many solutions.

Option C; The equations y = –3x + 4 and y = - 1/3x + 4 are most certainly not the same provided the second equation has a slope of - 1 /3 comparative to that of the first equation's slope, - 3.

Option D; y = –3x + 4 and y = –6x + 8, are one in the same, as if yoy multiply the first equation by 2 you receive the second; y = –6x + 8

Solution( s ); y = – 3x + 4 and 3y = – 9x + 12, y = –3x + 4 and y = –6x + 8

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.