Math HELP!?

Question

1. y = -x – 2
y = x + 3


(1 point)
(3, 0)
(-3, 1)
infinitely many solutions
no solution
2. y = -x + 3
y = 2x – 6

(1 point)
(3, 0)
(-3, 1)
infinitely many solutions
no solution

Answer 1

y = -x – 2
y = x + 3

add the 2 equations to get
2y = -2 +3 = 1
y = 1/2 ----> x = y -3 = 1/2 -3 = -5/2
solution (-5/2 , 1/2).

As you can see these are 2 equations of 2 lines:
y = -x – 2 , (slope = -1)
y = x + 3, (slope = 1)
These 2 lines are perpendicular to each other, they interesect at only one point, which is the solution.

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y = -x + 3 , call this eq1
y = 2x – 6 , call this eq2
substract eq1 from eq2 to get
y-y = 2x -6 -(-x +3) = 2x -6 +x -3
0 = 3x -9 ---> x =3
y = -x +3 = -3 +3 = 0
Solution = (3, 0)

Answer 2

You must have copied the first one incorrectly because the answer is not on your list.

y= -x - 2
y= x + 3
So -x - 2 = x + 3
or -2x = 5
and x = -5/2 or -2 1/2 and y = x + 3 or 1/2

The second one is easier once you set -x + 3 = 2x -6.
Remeber to add the opposite of a number to move it to the other side (example: adding 6 to each side will leave you with -x + 3 +6 = 2x -6 +6 or -x + 9 = 2x). Next you would add the X to each side in order to cancel it out of one side.

Answer 3

1. y = -x – 2
y = x + 3
-x-2=x+3 --> -2x = 5 --> x = -2.5
None of the answers given is correct

2 y= -x+3
y= 2x -6
-x+3 = 2x-6 --> -3x=-9 --> x = 3
(3,0) is correct answer.