Question

2x - y = 10
y = -x - 1
Solve the system of equations

(9, 8) correct?

(3, -4)

no solution

Answer 1

you're correct

Answer 2

thanks

Answer 3

No, that is NOT correct.

\[2x-y=10\]\[2(9)-8 = 10\]Works
\[y=-x-1\]\[8=-9-1\]\[8=-10\]Does not work
Must satisfy ALL equations in the system to be a valid solution.

rearrange second equation:\[y=-x-1\]\[x+y=-1\]

\[2x-y=10\]\[x+y=-1\]Add equations together
\[2x+x + y - y = 10 -1\]\[3x + 0y = 9\]\[x = 3\]\[x+y=-1\]\[3+y=-1\]\[y = -4\]

Testing:
\[2x-y=10\]\[2(3)-(-4) = 10\]\[6+4=10\checkmark\]
\[y=-x-1\]\[(-4)=-(3)-1\]\[-4=-4\checkmark\]
Therefore \((3,-4\)) is the solution.

Alternative solution by substitution:

\[2x-y=10\]\[y=-x-1\]Substitute \((-x-1)\) everywhere you see \(y\) in the first equation\[2x-(-x-1) = 10\]\[2x+x + 1 = 10\]\[3x+1=10\]\[3x=9\]\[x=3\]\[y=-x-1 = -(3)-1 = -4\]\((3,-4)\) is solution (not checking it again because I already che