How many solutions does the following system have?

y=2x-12
y=3x+12

One solution if the coefficients of x or/and y are different in the simplest form of the two equations
Infinite many solutions if the coefficients of x , y and the numerical terms are equal in the simplest form of the two equations
No solution if the coefficients of x and y are equal and the numerical terms are different in the simplest form of the two equations

The system of equations is:

y = 2x - 12 ⇒ (1)

y = 3x + 12 ⇒ (2)

∵ The equations are in its simplest form

∵ The coefficients of x in the two equations are different

- That is the 1st case above

∴ The system has one solution

Let us prove that by solving the system

To solve the system of equations equate (1) and (2) to find x

∵ 3x + 12 = 2x - 12

- Subtract 2x from both sides

∴ x + 12 = -12

- Subtract -12 from both sides

∴ x = -24

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

∵ y = 3(-24) + 12

∴ y = -72 + 12

∴ y = -60

∴ The solution of the system is (-24 , -60)

The system has one solution

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