To find the solution to a system of equations, we need to substitute the given solution (-2, 1) into both equations and see if it satisfies them.
Let's check each equation pair:
1) y = -2x - 2
2x - 2y = 5
Substitute x = -2 and y = 1 into the equations:
1) 1 = -2(-2) - 2
1 = 4 - 2
1 = 2 (Doesn't satisfy the equation)
2) 2(-2) - 2(1) = 5
-4 - 2 = 5
-6 = 5 (Doesn't satisfy the equation)
Therefore, this system of equations does not have the solution (-2, 1).
2) 2x - y = -5
x + 2y = 10
Substitute x = -2 and y = 1 into the equations:
1) 2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5 (Satisfies the equation)
2) -2 + 2(1) = 10
-2 + 2 = 10
0 = 10 (Doesn't satisfy the equation)
Therefore, this system of equations does not have the solution (-2, 1).
3) x - 4y = 8
3x + 10 = -2y
Substitute x = -2 and y = 1 into the equations:
1) -2 - 4(1) = 8
-2 - 4 = 8
-6 = 8 (Doesn't satisfy the equation)
2) 3(-2) + 10 = -2(1)
-6 + 10 = -2
4 = -2 (Doesn't satisfy the equation)
Therefore, this system of equations does not have the solution (-2, 1).
4) y = -3/2x - 2
2x - y = -5
Substitute x = -2 and y = 1 into the equations:
1) 1 = -3/2(-2) - 2
1 = 3 + 2
1 = 5 (Doesn't satisfy the equation)
2) 2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5 (Satisfies the equation)
Therefore, the system of equations y = -3/2x - 2 and 2x - y = -5 has the solution (-2, 1).
Which of the following systems of equations has the solution (-2, 1)?
This question requires you to show your work.
(1 point)
Responses
y=−2x−2 and 2x−2y=5
y is equal to negative 2 x minus 2 and 2 x minus 2 y is equal to 5
2x−y=−5 and x+2y=10
2 x minus y is equal to negative 5 and x plus 2 y is equal to 10
x−4y=8 and 3x+10=−2y
x minus 4 y is equal to 8 and 3 x plus 10 is equal to negative 2 y
y=−32x−2 and 2x−y=−5
1 answer