for each ordered pair, determine whether it a solution to the systems of equations
-14x+2y=-8
y=7x-4
(x,y) is it a solution? yes/no
(0,4)
(3,17)
(-1, -11)
(-2,5)
To determine whether each ordered pair is a solution to the system of equations, we substitute the values of x and y into each equation and check if the equations hold true.
For the first ordered pair (0, 4):
-14(0) + 2(4) = -8 --> 0 + 8 = -8 --> 8 = -8 // This equation is false
y = 7(0) - 4 --> 0 - 4 = -4 // This equation is true
Since the first equation is false, (0, 4) is not a solution to the system of equations.
For the second ordered pair (3, 17):
-14(3) + 2(17) = -8 --> -42 + 34 = -8 --> -8 = -8 // This equation is true
y = 7(3) - 4 --> 21 - 4 = 17 // This equation is true
Since both equations are true, (3, 17) is a solution to the system of equations.
For the third ordered pair (-1, -11):
-14(-1) + 2(-11) = -8 --> 14 - 22 = -8 --> -8 = -8 // This equation is true
y = 7(-1) - 4 --> -7 - 4 = -11 // This equation is true
Since both equations are true, (-1, -11) is a solution to the system of equations.
For the fourth ordered pair (-2, 5):
-14(-2) + 2(5) = -8 --> 28 + 10 = -8 --> 38 = -8 // This equation is false
y = 7(-2) - 4 --> -14 - 4 = -18 // This equation is false
Since both equations are false, (-2, 5) is not a solution to the system of equations.
To summarize:
(0, 4) is not a solution,
(3, 17) and (-1, -11) are solutions, and
(-2, 5) is not a solution.