Hello!
In this question, we are asked to find which set of points are solutions to our equation: 7x + 4y = -23
In order to find which points are solutions to our equation, we will plug the values into our equation and solve. If both sides of the equation are equal, the point will be a solution.
Note: Our coordinate point is in the format of (x,y), so we will plug in the values according to its variable.
Solve:
(-1,-4):
Plug in coordinate.
7(-1) + 4(-4) = -23
Simplify.
-7 - 16 = -23
-23 = -23
Since it is equal, (-1,-4) is a solution.
(2,6):
Plug in coordinate.
7(2) + 4(6) = -23
Simplify.
14 + 24 = -23
38 = -23
Since it is not equal, making it false, (2,6) is not a solution.
(-5,3):
Plug in coordinate.
7(-5) + 4(3) = -23
Simplify.
-35 + 12 = -23
-23 = -23
Since it is equal, (-5,3) is a solution.
(6,-7):
Plug in coordinate.
7(6) + 4(-7) = -23
Simplify.
42 - 28 = -23
14 = -23
Since it is not equal, making it false, (6,-7) is not a solution.
Answer:
The solutions to the equation are: (-1,-4) and (-5,3).