Question

How many solutions does this system have?

6x+3y--12
y--2x+4
one
two
an infinite number
no solution

Answer 1

Answer: ONE

Explanation:

I am going to use substitution method to solve for x.

6x + 3y = 12 and y = 2x + 4

--> 6x + 3(2x + 4) = 12

6x + 6x + 12 = 12

12x + 12 = 12

12x = 0

x
`=(0)/(12)`

x = 0

Plug the x-value into y = 2x + 4 to solve for y:

y = 2(0) + 4

y = 0 + 4

y = 4

There is ONE solution, which is (0, 4)

Answer 2

one solution ⇒ 1st answer

Explanation:

* Lets explain how to solve the question

- The 1st equation is 6x + 3y = 12

- The 2nd equation is y = 2x + 4

- To solve the two equation substitute y in the 1st equation by the

2nd equation

∴ 6x + 3(2x + 4) = 12

- Multiply 3x by the bracket (2x + 4)

∴ 6x + 6x + 12 = 12

- Subtract 12 from both sides

∴ 12x = 0

- Divide both sides by 12

∴ x = 0

- Substitute the value of x in the 2nd equation

∴ y = 2(0) + 4

∴ y = 4

∴ The solution is (0 , 4)

* There is one solution for this system