Which of the following systems of equations has the solution (-2, 1)? This question requires you to show your work. (1 point) Responses
x−4y=8 and 3x+10=−2y
y=−3/2x−2 and 2x−y=−5
2x−y=−5 and x+2y=10
y=−2x−2 and 2x−2y=5
show your work. do not use matrix form
To find the solution to each system of equations, we substitute the x-value (-2) and y-value (1) into each equation to see if they are satisfied.
1. x − 4y = 8
-2 − 4(1) = 8
-2 - 4 = 8
-6 ≠ 8
3x + 10 = -2y
3(-2) + 10 ≠ -2(1)
-6 + 10 ≠ -2
4 ≠ -2
Since the values do not match, the solution (-2, 1) is not a solution to this system of equations.
2. y = -3/2x - 2
1 = -3/2(-2) - 2
1 = 3 + 2
1 = 5 (incorrect)
2x - y = -5
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5 (correct)
Since only one of the equations is satisfied, this system does not have the solution (-2, 1).
3. 2x - y = -5
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5 (correct)
x + 2y = 10
(-2) + 2(1) = 10
-2 + 2 = 10
0 ≠ 10
Since only one of the equations is satisfied, this system does not have the solution (-2, 1).
4. y = -2x - 2
1 = -2(-2) - 2
1 = 4 - 2
1 = 2 (incorrect)
2x - 2y = 5
2(-2) - 2(1) = 5
-4 - 2 ≠ 5
-6 ≠ 5
Since the values do not match, the solution (-2, 1) is not a solution to this system of equations.
Therefore, none of the given systems of equations have the solution (-2, 1).