Which of the following systems of equations has the solution (-2, 1)?%0D%0A%0D%0AThis question requires you to show your work.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Ay=−32x−2%0D%0A%0D%0A=%0D%0A−%0D%0A3%0D%0A2%0D%0A%0D%0A−%0D%0A2%0D%0A and 2x−y=−5%0D%0A2%0D%0A%0D%0A−%0D%0A%0D%0A=%0D%0A−%0D%0A5%0D%0Ay is equal to negative 3 over 2 x minus 2 and 2 x minus y is equal to negative 5%0D%0A%0D%0Ax−4y=8%0D%0A%0D%0A−%0D%0A4%0D%0A%0D%0A=%0D%0A8%0D%0A and 3x+10=−2y%0D%0A3%0D%0A%0D%0A+%0D%0A10%0D%0A=%0D%0A−%0D%0A2%0D%0A%0D%0Ax minus 4 y is equal to 8 and 3 x plus 10 is equal to negative 2 y%0D%0A%0D%0A2x−y=−5%0D%0A2%0D%0A%0D%0A−%0D%0A%0D%0A=%0D%0A−%0D%0A5%0D%0A and x+2y=10%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A10%0D%0A2 x minus y is equal to negative 5 and x plus 2 y is equal to 10%0D%0A%0D%0Ay=−2x−2%0D%0A%0D%0A=%0D%0A−%0D%0A2%0D%0A%0D%0A−%0D%0A2%0D%0A and 2x−2y=5
To find out which system of equations has the solution (-2, 1), we need to substitute x = -2 and y = 1 into each system of equations and check if they satisfy all the equations.
1. y = -3/2x - 2 and 2x - y = -5
Substitute x = -2 and y = 1:
1 = -3/2(-2) - 2
1 = 3 + 2
1 = 5 (Not true)
2(-2) -1 = -5
-4 - 1 = -5
-5 = -5 (True)
Therefore, the correct system of equations is:
2x - y = -5
So, the correct answer is:
y = -2x - 2 and 2x - 2y = 5