for each ordered pair, determine whether it a solution to the systems of equations
-3x+2y=5
2x+7y=8
(x,y) is it a solution? yes/no
(-7,-8)
(4,0)
(-3,-2)
(5,4)
this is the correct answers
Apologies for the mistake. Here are the correct answers:
(-7, -8) is not a solution to the system of equations.
(4, 0) is not a solution to the system of equations.
(-3, -2) is a solution to the system of equations.
(5, 4) is a solution to the system of equations.
To determine whether each ordered pair is a solution to the system of equations, we can substitute the values of x and y into both equations and check if the equations hold true.
For the first ordered pair (-7, -8):
-3(-7) + 2(-8) = 21 -16 = 5
2(-7) + 7(-8) = -14 - 56 = -70
The values do not satisfy the equations, so (-7, -8) is not a solution to the system of equations.
For the second ordered pair (4, 0):
-3(4) + 2(0) = -12 + 0 = -12
2(4) + 7(0) = 8 + 0 = 8
The values satisfy the equations, so (4, 0) is a solution to the system of equations.
For the third ordered pair (-3, -2):
-3(-3) + 2(-2) = 9 - 4 = 5
2(-3) + 7(-2) = -6 - 14 = -20
The values do not satisfy the equations, so (-3, -2) is not a solution to the system of equations.
For the fourth ordered pair (5, 4):
-3(5) + 2(4) = -15 + 8 = -7
2(5) + 7(4) = 10 + 28 = 38
The values do not satisfy the equations, so (5, 4) is not a solution to the system of equations.
Therefore, the solutions are:
(-7, -8) - No
(4, 0) - Yes
(-3, -2) - No
(5, 4) - No