Question

which of the following systems of equations has the solution (-2, 1)

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

Answer 1

So what one is the answer

Answer 2

Why is that correct?

Answer 3

2. y = -2x - 2 and 2x - 2y = 5

To find the solution, we plug x = -2 into both equations:
y = -2(-2) - 2
y = 4 - 2
y = 2

Now we plug x = -2, y = 2 into the second equation:
2(-2) - 2(2) = 5
-4 - 4 = 5
-8 ≠ 5

Hence, the solution is not (-2, 1) so we rule out this equation.

Next, we try the equation with two variables:
3. y = -3/2 x - 2 and 2x - y = -5

Substitute x = -2 into:
y = -3/2(-2) - 2
y = 3 - 2
y = 1

Substitute x = -2, y = 1 into the second equation:
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5

Since the solution (-2, 1) works for the third system, we identify that it is the correct one.

Answer 4

The system of equations that has the solution (-2, 1) is:

y = -3/2 x - 2
2x - y = -5

Therefore, option 3 is the correct answer.

Answer 5

To verify that the solution (-2, 1) works for the system of equations:

Substitute x = -2 into the first equation:
y = -3/2 (-2) - 2
y = 3 + 2
y = 1

Now, confirm x = -2, y = 1 in the second equation:
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5

Since the solution (-2, 1) satisfies both equations simultaneously, the correct system of equations is:
y = -3/2 x - 2
2x - y = -5

Therefore, option 3 is indeed the correct answer. Thank you for the question.