Question

Determine if each ordered pair is a solution to the given system. 3x-2y=-9 6x+2y=18

a. 1,6
b. -5,-3

Answer 1

To determine if each ordered pair is a solution to the given system, substitute the values of x and y from each ordered pair into the equations and check if the equations are true. Neither of the ordered pairs, (1, 6) and (-5, -3), is a solution to the given system of equations.

Step-by-step explanation:

To determine if each ordered pair is a solution to the given system of equations, we can substitute the values of x and y from each ordered pair into the equations and check if the equations are true. Let's start with the first ordered pair, (1, 6).

1. Substituting x = 1 and y = 6 into the first equation, we get: 3(1) - 2(6) = -3 - 12 = -15.
2. Substituting x = 1 and y = 6 into the second equation, we get: 6(1) + 2(6) = 6 + 12 = 18.
3. Since the first equation is not true for this ordered pair (-15 ≠ -9), (1, 6) is not a solution to the given system of equations.
4. Now let's check the second ordered pair, (-5, -3).
5. Substituting x = -5 and y = -3 into the first equation, we get: 3(-5) - 2(-3) = -15 + 6 = -9.
6. Substituting x = -5 and y = -3 into the second equation, we get: 6(-5) + 2(-3) = -30 - 6 = -36.
7. Since neither equation is true for this ordered pair (-9 ≠ -9 and -36 ≠ 18), (-5, -3) is not a solution to the given system of equations.

Therefore, neither of the ordered pairs, (1, 6) and (-5, -3), is a solution to the given system of equations.