Which of the following points is a solution to the system of equations:
x−2y=−19
5x+2y=1
(1 point)
Responses
(1,−2)
open paren 1 comma negative 2 close paren
(−3,8)
open paren negative 3 comma 8 close paren
(1,2)
open paren 1 comma 2 close paren
(5,12)
To find the solutions of the system of equations, we need to substitute the x and y values of each point into both equations and check if they satisfy them.
Let's check each point:
1) Substitute x = 1 and y = -2 into the equations:
Equation 1: x - 2y = -19
1 - 2(-2) = -19
1 + 4 = -19
5 = -19
Equation 2: 5x + 2y = 1
5(1) + 2(-2) = 1
5 - 4 = 1
1 = 1
Since the first point does not satisfy the first equation, it is not a solution to the system of equations.
2) Substitute x = -3 and y = 8 into the equations:
Equation 1: x - 2y = -19
-3 - 2(8) = -19
-3 - 16 = -19
-19 = -19
Equation 2: 5x + 2y = 1
5(-3) + 2(8) = 1
-15 + 16 = 1
1 = 1
The second point satisfies both equations, so it is a solution to the system of equations.
3) Substitute x = 1 and y = 2 into the equations:
Equation 1: x - 2y = -19
1 - 2(2) = -19
1 - 4 = -19
-3 = -19
Equation 2: 5x + 2y = 1
5(1) + 2(2) = 1
5 + 4 = 1
9 = 1
The third point does not satisfy the second equation, so it is not a solution to the system of equations.
4) Substitute x = 5 and y = 12 into the equations:
Equation 1: x - 2y = -19
5 - 2(12) = -19
5 - 24 = -19
-19 = -19
Equation 2: 5x + 2y = 1
5(5) + 2(12) = 1
25 + 24 = 1
49 = 1
The fourth point does not satisfy the second equation, so it is not a solution to the system of equations.
Therefore, the only solution to the system of equations is (-3, 8).