for each ordered pair, determine whether it a solution to the systems of equations
-7x+2y=3
2x-3y=4
(x,y) is it a solution? yes/no
(-3,-9)
(8,4)
(0,5)
(-2,-1)
To determine whether each ordered pair is a solution to the system of equations, we substitute the x and y values into the equations and check if the equations hold true.
For the system of equations:
-7x + 2y = 3
2x - 3y = 4
1. For the ordered pair (-3, -9):
Substituting x = -3 and y = -9 into the equations:
-7(-3) + 2(-9) = 3
21 - 18 = 3
3 = 3
2(-3) - 3(-9) = 4
-6 + 27 = 4
21 = 4
The equation 21 = 4 is not true, so (-3, -9) is not a solution to the system of equations.
2. For the ordered pair (8, 4):
Substituting x = 8 and y = 4 into the equations:
-7(8) + 2(4) = 3
-56 + 8 = 3
-48 = 3
2(8) - 3(4) = 4
16 - 12 = 4
4 = 4
The equation -48 = 3 is not true, so (8, 4) is not a solution to the system of equations.
3. For the ordered pair (0, 5):
Substituting x = 0 and y = 5 into the equations:
-7(0) + 2(5) = 3
0 + 10 = 3
10 = 3
2(0) - 3(5) = 4
0 - 15 = 4
-15 = 4
The equation 10 = 3 is not true, so (0, 5) is not a solution to the system of equations.
4. For the ordered pair (-2, -1):
Substituting x = -2 and y = -1 into the equations:
-7(-2) + 2(-1) = 3
14 - 2 = 3
12 = 3
2(-2) - 3(-1) = 4
-4 + 3 = 4
-1 = 4
The equation -1 = 4 is not true, so (-2, -1) is not a solution to the system of equations.
Therefore, the answer is:
No, (-3, -9) is not a solution.
No, (8, 4) is not a solution.
No, (0, 5) is not a solution.
No, (-2, -1) is not a solution.