1. An Algebra 1 Question

Hello all, thank you for your time.

Solve the system:

-x+3y=-1
x+2y=4

I understand how to do this, but my answer was not correct, the book said the answer was:
(14/5,3/5) but I have no idea how it got that. I must have made an error in my work, but I'm not sure where.

I started with x+2y=4 Subtracting 2y makes x=4-2y

Then you plug that into the other equation and you get

-4-2y+3y= -1
Which simplifies to:
-4+y=-1
y=3
Plugging that into the other one:
x+2x3=4
Which simplifies to:
x+6=4
Subtract six:
x=-2

Which gives an answer of (-2,3) but I know this is not corrrect because it does not work when you plug that into x and y for the original two sets.

Where am I making my error here?

Thank you very much

2. You made your error on the first step. Given $x = 4 - 2y$ and $-x + 3y = -1$, you can substitute for x into the second equation: $-(4 - 2y) + 3y = -1$. This gives you $-4 + 2y + 3y = -1$, or $5y - 4 = -1$.

3. Okay, just to make sure, same kind of problem with the -x thing i messed up

Write the equation of the line that is parallel to line A and passes through Point P

Line A=

$y= -x+4$

Point P= (-1,2)

That would be:
$y=-2-b$ right?
Originally it would be +b (y=mx+b) but since it's -x the + changes to a - correct?
If so, it would be
$2=-2-b$
$4=-b$
$4=b$

$y=2x-4$

correct?

At the end I wrote

$4=-b$
then
$-4=b$
so
$y=2x-4$

Forgot the negative on the second one

5. Write the equation of the line that is parallel to line A and passes through Point P

Line A=

Point P= (-1,2)
A line parallel to A has the form y=-x +b.

Substitute the x and y values of point P for x and y to find b.