Question

do the Two systems of equations shown have the same solution?
4x+y=−1
x+y=2

8x+2y=−2
−4x+1y=−8

Answer 1

To determine if the two systems of equations have the same solution, we can solve each system and compare the solutions.

1) For the first system of equations:
4x + y = -1
x + y = 2

Rearranging the second equation, we have:
y = 2 - x

Substituting this value of y into the first equation:
4x + (2 - x) = -1
3x + 2 = -1
3x = -3
x = -1

Plugging this value of x back into the second equation:
-1 + y = 2
y = 3

Therefore, the solution to the first system is x = -1, y = 3.

2) For the second system of equations:
8x + 2y = -2
-4x + y = -8

Rearranging the second equation, we have:
y = -8 + 4x

Substituting this value of y into the first equation:
8x + 2(-8 + 4x) = -2
8x - 16 + 8x = -2
16x - 16 = -2
16x = 14
x = 14/16
x = 7/8

Plugging this value of x back into the second equation:
-4(7/8) + y = -8
-7 + y = -8
y = -8 + 7
y = -1

Therefore, the solution to the second system is x = 7/8, y = -1.

Since the solutions to the two systems are different, the two systems of equations do not have the same solution.