Question

How many solutions does this system have?

Answer 1

Answer:

one solution

Step-by-step explanation:

* Lets start to solve the question

- The 1st equation x - y = -4

- The 2nd equation 3x + y = 8

- We will use the elimination method to solve this system of equation

∵ x - y = -4 ⇒ (1)

∵ 3x + y = 8 ⇒ (2)

- Add the two equation (1) and (2) to eliminate y

∴ x + 3x = -4 + 8

∴ 4x = 4

- Divide both sides by 4

∴ x = 1

- Substitute the value of x in equation (1) or equation (2) to find

  the value of y

- We will use equation (1)

∴ 1 - y = -4

Subtract 1 from both sides

∴ -y = -5

- Divide both sides by -1

∴ y = 5

∴ The solution is (1 , 5)

* The system has one solution

Answer 2

Answer:  ONE

Step-by-step explanation:

I am going to use elimination method to solve for x. Since they already have an opposite coefficient for y, I can add the two equations to eliminate y.

 x - y = -4    

3x + y = 8  

4x       = 4

 x       $=\dfrac{4}{4}$

 x       = 1

Substitute x with 1 in either of the equations to solve for y:

3(1) + y = 8

 3  + y = 8

        y = 5

Therefore, there is ONE solution, which is (1, 5).