Choose the correct words from the drop-down menu to make a true statement about the system of equations.
y = { x + 2
-x + 3y = 6
using substitution, the system has


a . infinitely many solutions

b. no solution

c. one solution

C. It has only one solution

Step-by-step explanation:

The system of equations is expressed as

y = x + 2

Subtracting 2 from the left hand side and the right hand side of the equation, it becomes

x = y - 2 - - - - - - - - - 1

-x + 3y = 6

Multiplying the left hand side and the right hand side of the equation by - 1, it becomes

x - 3y = - 6

Adding 3y to the left hand side and the right hand side of the equation, it becomes

x = 3y - 6 - - - - - - - - 2

Equating equation 1 and equation 2, it becomes

y - 2 = 3y - 6

3y - y = - 2 + 6

2y = 4

y = 4/2 = 2

Substituting y = 2 into equation 1, it becomes

x = 2 - 2 = 0

The solutions are (0, 2)

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