Question

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
Choose...

A . infinitely many solutions

B. no solution

C. one solution

Answer 1

Answer:C. It has only one solution

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)