Yes, both systems of equations have the same solution. Solving the first system:
4x + y = -1
x + y = 2
Rearranging the second equation:
y = 2 - x
Substituting this into the first equation:
4x + (2 - x) = -1
3x + 2 = -1
3x = -3
x = -1
Substituting the value of x back into the second equation:
-1 + y = 2
y = 3
So the solution for the first system is x = -1 and y = 3.
Now solving the second system:
8x + 2y = -2
-4x - 4y = -8
Rearranging the second equation:
4x + 4y = 8
Dividing both sides of the equation by 4:
x + y = 2
Comparing this equation to the second equation of the first system, we can see that they are the same equation. Therefore, the second system also has x = -1 and y = 3 as the solution. Consequently, both systems 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+-4y=−8
1 answer