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# subtitution and Elimination #3b

1)  y=-5x+2
y=3x-14

2)  x+y=0
5x+y=4

1)

y = -5x + 2
y = 3x - 14

Set them both equal to each other since both are equal to y.

-5x + 2 = 3x - 14
+5x         +5x

2 = 8x -14
+14    +14

16 = 8x

x = 2

y = 3(2)- 14 = -8

2)
x+y=0
5x+y=4
---------
Multiply the top by -1

-x - y = 0
5x + y = 4

5x-x = 4x, y - y = 0, 4 + 0 = 4
4x = 4
x = 1

5(1) + y = 4
5 + y = 4
-5        -5

y = -1

Hi Jason.  thanks for your answers, but I don't understand #2 at all.  Why multiply by -1,and what do you multiply?   then I don't know how you even got the equations.   Please explain.
You multiply the top equation by -1 so that the y's will sum to 0 (cancel out) when you add the two equations together.

x + y = 0
5x + y = 4

(-1)(x) + (-1)(y) = (-1)(0)

-x - y     =    0
+ (5x + y)  = + 4
---------------------

5x-1x = 4x
y-y = 0
4+0  = 4

So
4x + 0  = 4
4x = 4

Divide both sides by 4.

4x/4 = 4/4

x = 1

Now plug 1 in for x:
x + y = 0

1 + y = 0

Subtract 1 from both sides:

1 + y -1 = 0-1
y = -1

Thanks again!  Jason, having a real hard time using the method I now know with this last one, can you help? I've been at it for about an hour now.
-1/2x-1/4y=3
1/3x+1/6y=2

Multiply the top equation by 4 and the bottom by 6.

-2x - y = 12
2x + y = 12

Add them together and you get:

0 = 24.  This is always false.

Therefore, no solution is possible.

Note also that if you change them to y = mx+b format:
y = -2x - 12
y = -2x + 12

Since the slopes are the same, they are parallel and never intersect.  Thus, the "No solution" answer is correct.

Have a great day.