Question

Select ALL statements that are true.

2x+8y=12

1/2x+3y=6


Question 5 options:

(6,1) makes the first equation true (an identity) and the second equation false (not an identity). It is NOT a solution to the system.


(6,1) makes the first equation false (not an identity) and the second equation true (an identity). It is NOT a solution to the system.


(6,1) makes both the first equation and the second equation true (an identity). It IS a solution to the system.


(-6,3) makes the first equation false (not an identity) and the second equation true (an identity). It is NOT a solution to the system.


(-6,3) makes the first equation false (not an identity) and the second equation true (an identity). It is NOT a solution to the system.


(-6,3) makes both the first equation and the second equation true (an identity). It IS a solution to the system.

Answer 1

• (6,1) makes the first equation false (not an identity) and the second equation true (an identity). It is NOT a solution to the system.
• (-6,3) makes both the first equation and the second equation true (an identity). It IS a solution to the system.

Explanation:

Consider an ordered pair
`(x,y)` and when the values of
`x` and
`y` are substituted into an equation. If the result is a true statement, then it makes the equation true. Otherwise, it makes the equation false.

For the pair to be a solution to the system, the ordered pair must make both equations true.