How many solutions does this system of equations have? A. No Solutions
B. 2
C. 1
D. An infinite number of solutions

Explanation:

Let's solve the first equation for y

4x - 2y = 6

4x-6 = 2y

2y = 4x-6

y = (4x-6)/2

y = (4x/2) - (6/2)

y = 2x - 3

After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3

Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).

Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.

You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.

Here's another approach using substitution

4x - 2y = 6 ... start with the first equation

4x - 2( y ) = 6

4x - 2( 2x-3 ) = 6 replace y with 2x-3; ie plug in y = 2x-3

4x - 2(2x) - 2(-3) = 6

4x - 4x + 6 = 6

0x + 6 = 6

0 + 6 = 6

6 = 6

We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.

Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.