Final answer:
To determine whether each ordered pair is a solution to the system of equations, substitute the values of x and y from each pair into the given equations and check if the equations are satisfied.
Only (-1, -13) and (2, 5) are solutions to the system of equations.
Step-by-step explanation:
Substituting the values of x and y from each pair into the given equations and check if the equations are satisfied.
=> For the ordered pair (0, -4), substituting x = 0 and y = -4 into the equations, we get:
y = 6(0) - 7 = -7, which does not match -4.
And 9(0) - 2(-4) = 8, which matches 8.
Therefore, (0, -4) is not a solution to the system of equations.
=> For the ordered pair (-1, -13), substituting x = -1 and y = -13 into the equations, we get:
y = 6(-1) - 7 = -13, which matches -13.
And 9(-1) - 2(-13) = 8, which matches 8.
Therefore, (-1, -13) is a solution to the system of equations.
=> For the ordered pair (-5, 3), substituting x = -5 and y = 3 into the equations, we get:
y = 6(-5) - 7 = -37, which does not match 3.
And 9(-5) - 2(3) = -49, which does not match 8.
Therefore, (-5, 3) is not a solution to the system of equations.
=> For the ordered pair (2, 5), substituting x = 2 and y = 5 into the equations, we get:
y = 6(2) - 7 = 5, which matches 5.
And 9(2) - 2(5) = 8, which matches 8.
Therefore, (2, 5) is a solution to the system of equations.