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)

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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