SOLUTION: -x + y = 4 2x - 5y = -14 I am completely stuck on how to go about doing this problem. I know that the Solutions x and y are always intergers between 5 and -5. Each time i

Click here to see ALL problems on Linear-systems

Question 149211: -x + y = 4
2x - 5y = -14
I am completely stuck on how to go about doing this problem.
I know that the Solutions x and y are always intergers between 5 and -5.
Each time i try I come up with No Solution.
But I am being told that is wrong.
x = ?
Y = ?
If you could, please show me a few steps on How to get the answer
to this problem.
I would greatly appreciate your help
Thank You,
Kerry G.
Found 2 solutions by Fombitz, josmiceli:
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
There are several methods to solve this system of linear equations.
We could graph both lines and look for the intersection point.
Put both into slope-intercept form, , and then graph.

Looks like a solution exists at (-2,2).
Although this method worked for this system, it's not always clear what the exact answer is.
The graphical method explains what you're really trying to do, find where lines intersect, if they do.
We'll work it out using the substitution method, to get an exact answer.
1.
2.
Use eq. 1 to get the variable y as an expression with x.
1.

Now substitute this expression into eq. 2 and solve for x,
2.

Now back substitute into eq. 1 or 2 to solve for y,

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The basics:
You have 2 equations and 2 unknowns x, and y
In that situation, you can ALWAYS solve for the unknowns
Even if you had 30 equations and 30 unknowns, it would be
more difficult, but you could still solve for each of
your unknowns
----------------------------------------------
In this problem you can use the simple laws of algebra
to solve for x and y, mainly:
Whatever you do to one side of the equation, you MUST
do the same thing to the other side in order for the
equation to still be true
----------------------------------------------

Add to both sides

On the left side, the 's cancel

That's what I want: one of the unknowns all by itself
Now I can replace in the other equation with
because it equals

Now I carry out the multiplication

Multiply both sides by

Subtract from both sides

Now substitute this value for back into either
of the equations

Subtract from both sides

The solutions are x = -2 and y = 2
Now check the answers:

and

OK