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.
do the Two systems of equations shown have the same solution?
4x+y=−1
x+y=2
8x+2y=−2
−4x+1y=−8
1 answer
1 answer