Question

20 points..Please Help!!

What does it mean for an equation to have no solution or infinite solutions? Identify the equation with one solution, infinite solutions and no solutions: (you don’t need to come up with an exact answer:
• 6y+2=3y+4
4x + 4y + 8 = x + y + 2
5x – 3 = 5x - 2

Answer 1

6y+2=3y+4 can be re-written as 3y = 2, so that y = 2/3. This equation has a solution, only one, unique solution.

4x + 4y + 8 = x + y + 2 could be re-written as

4(x+y) + 6 = 1(x+y), which could be simplified to 3(x+y) = -6, or x+y= -2
Here we have ONLY ONE equation in TWO unknowns. For any value of x we choose, there will be one corresponding value of y. This is a linear equation, and written in the usual form is y = -x -2.

5x – 3 = 5x - 2 could be simplified by subtr. 5x from both sides: -3 = -2. Obviously this is false, and so the equation 5x – 3 = 5x - 2 has no solution.

Answer 2

Hello!

If a problem has infinite solutions you will end with a 0, with one it will end with any number and for no solutions you will get a equations that does not equal each other

Ex: 5 = 9

You can do the bottom first since it looks the easiest.

5x - 3 = 5x - 2

subtract 5x from both sides

0x -3 = -2

Add 3 to both sides

0x = 1

0x
`\\eq 1`

So it has no solutions

Next you can do the top one

6y + 2 = 3y + 4

subtract 3y from both sides

3y + 2 = 4

Subtract 2 from both sides

3y = 2

Divide both sides by 3

y =
`(2)/(3)`

Since this came to a regular number it has one solution

The only one left has the be the one with infinite solutions by we can check

4x + 4y + 8 = x + y + 2

since the left side is the same as the right just multiplied by 4 it has infinite solutions

So the first one has one solution

The second one has infinite solutions

And the third one has no solutions

Hope this helps!