Question

Which statements are true about the ordered pair (-1,-4) and the system of equations?

x-y=3

7x-y=-3

Question 1 options:


When (-1,-4) is substituted into the first equation, the equation is false.


When (-1,-4) is substituted into the first equation, the equation is true.


When (-1,-4) is substituted into the second equation, the equation is false.


When (-1,-4) is substituted into the second equation, the equation is true.


The ordered pair (-1,-4) is a solution to the system of linear equations


The ordered pair (-1,-4) is not a solution to the system of linear equations.

Answer 1

When (-1,-4) is substituted into the first equation, the equation is true.

When (-1,-4) is substituted into the second equation, the equation is true.

Explanation:

The given system is

x-y=3

7x-y=-3

Make x the subject in the top equation to get:

x=y+3

Put x=y+3 in the bottom equation to get:

7(y+3)-y=-3

Expand

7y+21-y=-3

7y-y=-3-21

6y=-24

y=-4

Put y=-4 into x=y+3 to get

x=-4+3=-1

Hence the point (-1,-4) is a solution to both equation