Which of the following points is a solution to the system of equations:
x−2y=−19
5x+2y=1
(1 point)
Responses
(−3,8)
open paren negative 3 comma 8 close paren
(1,−2)
open paren 1 comma negative 2 close paren
(5,12)
(1,2)
To check if a point is a solution to a system of equations, we substitute the values of x and y into each equation and see if both equations are true. Let's test each point:
For point (−3,8):
x−2y=−19
-3 - 2(8) = -3 - 16 = -19 (true)
5x+2y=1
5(-3) + 2(8) = -15 + 16 = 1 (true)
For point (1,−2):
x−2y=−19
1 - 2(-2) = 1 + 4 = 5 (false)
5x+2y=1
5(1) + 2(-2) = 5 - 4 = 1 (true)
For point (5,12):
x−2y=−19
5 - 2(12) = 5 - 24 = -19 (true)
5x+2y=1
5(5) + 2(12) = 25 + 24 = 49 (false)
For point (1,2):
x−2y=−19
1 - 2(2) = 1 - 4 = -3 (false)
5x+2y=1
5(1) + 2(2) = 5 + 4 = 9 (false)
Therefore, the only point that is a solution to the system of equations is (−3,8).