Question

Which statements are true about thecordered pair (7,19) and the system of equations 2x-y=-5

Answer 1

I attached a screenshot for the complete question as well as the choices.

Answer:
The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false. 

Explanation:
A solution to the system is defined as the order pair which satisfies ALL the equation given in the system

The twp systems given are:
2x−y=−5 which can be rewritten as: y = 2x + 5
x+3y=22 which can be rewritten as 3y = 22 - x

the given point is (7,19). To know whether this point belongs to each of the given lines, we will substitute with the value of x in the line and calculate the corresponding y value. After that we will compare the calculated value with the given one to decide whether the point is a solution to the system or not.

1- For the first system:
y = 2x + 5
y = 2(7) + 5
y = 14 + 5
y = 19
The calculated value of y is the same as the given one. This means that this point is a solution to the first equation

2- For the second system:
3y = 22 - x
3y = 22 - 7
3y = 15
y = 5
The calculated value of y is not equal to the given one. This means that the given point is not a solution for the second equation.

Based on the above, we can note that the given pair satisfies the first equation, however, it does not satisfy the second one.
This means that it cannot be a solution to the system.

Hope this helps :)