determine whether left parenthesis negative 3 comma negative 1 right parenthesis
is a solution of the system:
3x + y=10
-5 + 2y= 13
Is left parenthesis negative 3 comma negative 1 right parenthesis
a solution of the system?
To determine if left parenthesis negative 3 comma negative 1 right parenthesis is a solution of the system, we need to substitute x = -3 and y = -1 into each equation and see if both equations are true.
Substituting x = -3 and y = -1 into 3x + y = 10, we get:
3(-3) + (-1) = -9 - 1 = -10
This equation is not true, since -10 does not equal 10. Therefore, left parenthesis negative 3 comma negative 1 right parenthesis is not a solution of the first equation.
Substituting x = -3 and y = -1 into -5 + 2y = 13, we get:
-5 + 2(-1) = -5 - 2 = -7
This equation is also not true, since -7 does not equal 13. Therefore, left parenthesis negative 3 comma negative 1 right parenthesis is not a solution of the second equation.
Since left parenthesis negative 3 comma negative 1 right parenthesis fails to satisfy both equations of the system, it is not a solution of the system.
To determine whether (-3, -1) is a solution of the system, we substitute the values of x and y into both equations and check if the equations hold true.
1) Substitute x = -3 and y = -1 into the first equation:
3(-3) + (-1) = 10
-9 - 1 = 10
-10 = 10 (False)
Since the first equation does not hold true when we substitute (-3, -1), we can conclude that (-3, -1) is not a solution of the system.