Choose the correct words from the drop-down menu to make a true statement about the system of equations. y = 1/3x + 2
–x + 3y = 6

Using substitution, the system has choose
A. No solution

B. One solution

C. Infinitely many solutions

C

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

- x + 3y = 6 → (2)

Substitute y = x + 2 into (2)

- x + 3( x + 2) = 6 ← distribute left side

- x + x + 6 = 6, that is

6 = 6 ← True

This statement indicates the system has infinitely many solutions

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.