Question

Which of the following systems of equations has the solution (-2, 1)?
show work

1. y=−3/2x−2 and 2x−y=−5
2. 2x−y=−5 and x+2y=10
3. x−4y=8 and 3x+10=−2y
4. y=−2x−2 and 2x−2y=5

Answer 1

there is 1 answer

Answer 2

To find the solution for each system of equations, we substitute (-2, 1) into each equation and check if it satisfies both equations.

1. y = -3/2x - 2
-2 = -3/2(-2) - 2
-2 = 3 + 2
-2 ≠ 1 (does not satisfy the first equation)

2. 2x - y = -5
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5 (satisfies the first equation)
x + 2y = 10
-2 + 2(1) = 10
-2 + 2 = 10
0 ≠ 10 (does not satisfy the second equation)

3. x - 4y = 8
-2 - 4(1)= 8
-2 - 4 = 8
-6 ≠ 8 (does not satisfy the first equation)

4. y = -2x - 2
1 = -2(-2) - 2
1 = 4 - 2
1 = 2 (does not satisfy the first equation)
2x - 2y = 5
2(-2) - 2(1) = 5
-4 - 2 = 5
-6 = 5
-6 ≠ 5 (does not satisfy the second equation)

Therefore, none of the given systems of equations has the solution (-2, 1).

Answer 3

Let's reevaluate the systems of equations:

1. y = -3/2x - 2 and 2x - y = -5
Substitute x = -2 and y = 1 into the first equation:
1 = (-3/2)(-2) - 2
1 = 3 - 2
1 = 1
This satisfies the first equation.

Substitute x = -2 and y = 1 into the second equation:
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5
This satisfies the second equation.

Therefore, the solution (-2, 1) satisfies this system of equations:
y = -3/2x - 2 and 2x - y = -5

The system of equations that has the solution (-2, 1) is:
1. y = -3/2x - 2 and 2x - y = -5