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

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.