The system has one solution
Step-by-step explanation:
Let us revise the type of the solutions of a system of equations
- 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
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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