Question

please help me !! helper will get a medal
Which of the following points is a solution to the system of equations shown?
y - x = -1
x + y = -5
a. (-3,-2) b. (-6,-1) c. (-2,-3)

Answer 1

The key is to rewrite this "in terms of one variable"
So step one is to find y in terms of x.

\[y-x=-1\]

\[y=-1+x\]

\[y=x-1\]

Answer 2

So another way of writing y is writing x-1

its like saying ok and okay
they look different but when it comes down to it they both mean the same thing.

So with this information we can rewrite the second equation "in terms of x"...

\[x+y=-5\]

Remember what we found out earlier:

y=x-1

So lets substitute y for x-1 so we have one variable instead of two. Thats the key for solving these.

Second equation rewritten in terms of x:
\[x+(x-1)=-5\]
Now Simplify:
\[x+x-1=-5\]
\[2x-1=-5\]
\[2x=-4\]
\[x=-2\]

Now you can use this information to plug your x-value back into your original equation the problem gives you to solve for y

\[y-x=-1\]
\[y-(-2)=-1\]
negative minus a number is positive
\[y+2=-1\]
\[y=-3\]

Answer: (-2, -3)

Answer 3

thank you so much!