To determine if a point is a solution to the system of equations, we substitute the values of the coordinates into each equation and check if both equations are satisfied.
Let's test each of the given points:
1) (5,12):
Substituting x = 5 and y = 12 into the first equation:
5 - 2(12) = -19
5 - 24 = -19
-19 = -19 (satisfied)
Substituting x = 5 and y = 12 into the second equation:
5(5) + 2(12) = 1
25 + 24 = 1
49 = 1 (not satisfied)
Since the second equation is not satisfied, (5,12) is not a solution to the system of equations.
2) (1,2):
Substituting x = 1 and y = 2 into the first equation:
1 - 2(2) = -19
1 - 4 = -19
-3 = -19 (not satisfied)
Substituting x = 1 and y = 2 into the second equation:
5(1) + 2(2) = 1
5 + 4 = 1
9 = 1 (not satisfied)
Since neither equation is satisfied, (1,2) is not a solution to the system of equations.
3) (-3,8):
Substituting x = -3 and y = 8 into the first equation:
-3 - 2(8) = -19
-3 -16 = -19
-19 = -19 (satisfied)
Substituting x = -3 and y = 8 into the second equation:
5(-3) + 2(8) = 1
-15 + 16 = 1
1 = 1 (satisfied)
Since both equations are satisfied, (-3,8) is a solution to the system of equations.
4) (1,-2):
Substituting x = 1 and y = -2 into the first equation:
1 - 2(-2) = -19
1 + 4 = -19
5 = -19 (not satisfied)
Substituting x = 1 and y = -2 into the second equation:
5(1) + 2(-2) = 1
5 - 4 = 1
1 = 1 (satisfied)
Since only one equation is satisfied, (1,-2) is not a solution to the system of equations.
Therefore, the solution to the system of equations is (-3,8).
Which of the following points is a solution to the system of equations: x−2y=−19 5x+2y=1 (1 point) Responses (5,12) open paren 5 comma 12 close paren (1,2) open paren 1 comma 2 close paren (−3,8) open paren negative 3 comma 8 close paren (1,−2)
1 answer
1 answer