Question

Please help with math question and please show ALL work.

1....How many solutions does the equation 3x+x+3=2(2x+1)+1 have?

2...How many solutions does the pair of equations have?

`4x+2y=60 \\ 12x+6y=180`

A. 0
B. 1
C. 2
D. infinitely many

Answer 1

1)
3x+x+3=2(2x+1)+1

Lets simplify it by first opening up the parenthesis.

3x+x+3=4x+2+1

Now lets add like terms :)

4x+3 = 4x+3

And since both sides equal to each other, we will have infinite solutions!

2)
4x+2y=60
12x+6y=180

You can notice that 12x+6y=180 is basically 3(4x+2y) = 3(60)

So that means it has infinitely many solutions.

Another way to check it would be to graph it. If you look the graph, you will notice that these two equations have the same line. So thus, it has infinitely many solutions. :)

Answer 2

1. Simplify first!

3x + x + 3 = 2(2x+1)+1
4x + 3 = 4x + 2 + 1
4x + 3 = 4x+3

Infinite solutions

2. Multiply both sides by three on the first equation and you will realize that these are the same equation. Because of this there are infinitely many solutions.