2w+3x-12=0 x+5w-13=0 substitution?

Question

show the working out so that i can uderstand it pleaser and then i can repeat it myself

Answer 1

2w+3x-12=0
x+5w-13=0

What you want to do, is use 1 formula to define x in terms of w (or vice versa), then substitute that definition into the other formula.

So, from formula #2:
x + 5w - 13 = 0
x = 13 - 5w

Substitute into formula #1:
2w+3x-12=0
2w+3(13 - 5w)-12=0
2w + 39 - 15w - 12 = 0
-13w + 27 = 0
-13w = -27
w = 27/13 = 2 1/13 (solution for W)

Now substitute the value for w into the formula for x to get the value of x:
x = 13 - 5w
x = 13 - 5 * 27/13 = 13 - 10 5/13 = 2 8/13 (solution for X)

Check:
2 * 2 1/13 + 3 * 2 8/13 - 12 = 0
4 2/13 + 7 11/13 - 12 = 0
0=0 (check!)

Answer 2

Take the 2nd equation: x + 5w - 13 = 0 and add 13 to both sides to get: x + 5w = 13

Then subtract 5w from each side to get: x = 13 - 5w

Now substitute "13 - 5w" in for "x" in the 1st equation:

2w + 3 (13 - 5w) = 0

Distribute the 3: 2w + 39 - 15w = 0

Combine the w's: -13w + 39 = 0

Subtract 39 from both sides: -13w = -39

Divide by -13: w = 3

Then substitute "3" in for "w" in either equation to find x.

I'll use the 2nd equation: x + 5 (3) = 0

Gives you: x + 15 = 0

Subtract 15 from both sides: x = -15

So your answers are x = -15 and w = 3

Hope that's clear enough.

Answer 3

Basically, you decide whether you want to substitute for w or x.

With the second equation, it is easy to move the second and third part to the other side to get x=13-5W.

Then you put that into the first equation to get

2w+3(13-5w) -12=0

Then you simplify to 2W +39-15w-12=0.

Then you simplify some more to get -13w+27=0

Move it around to get 27=13w or w=27/13 (if my arithmetic is correct)