Another troubling math question?

Question

solve ea. system by the substitution method. Indicated whether or not ea. system is independent, inconsistant, or dependent:
x-y=3
3x-2y=3
** Please be clear on how to do this step-by-step if possible, I have a bunch more questions like this one, and need to have a clear understanding of how in the world I do it. :)

Answer 1

I'll try and help you with this one and give you details on how to solve others.

To solve by substitution you must first solve for a single variable. Take the first equation, for example and solve for x.
x - y = 3

Add y to both sides:
x = y + 3

Now substitute this equation for x into the second equation:
3x - 2y = 3
3 (y+3) - 2y = 3

Multiply the 3 through:
3y + 9 - 2y = 3

Combine like terms:
(3y - 2y) + 9 = 3
y + 9 = 3

Subtract 9 from both sides:
y = 3 - 9
y = -6

Now solve for x by substituting this back into your original equation:
x - y = 3
x - (-6) = 3
x + 6 = 3
x = 3 - 6
x = -3

So your solution is x = -3, y = -6.

It's a good idea to double check your answer:
x - y =? 3
-3 - (-6) =? 3
-3 + 6 =? 3
3 = 3 <-- check

3x - 2y = 3
3(-3) - 2(-6) =? 3
-9 - (-12) =? 3
-9 + 12 =? 3
3 = 3 <-- check

Now to answer the second part of your question.

If you get to a solution with actual values (like we did) then you have an *independent* system of equations.

If you get to a solution like y = y or x = x or n = n, then you have a *dependent* system of equations. An example of this would be:
x = y + 1
2x = 2y + 2

Here you can see that the second equation is just double the first, so it doesn't give you any more information. If you substitute x = y + 1 into the second equation you get:
2(y + 1) = 2y + 2
2y + 2 = 2y + 2
2 = 2 <-- dependent system (x or y can be anything and the system is true)

The last case would be an *inconsistent* system. This is when you get to an answer like 2 = 7.
x = y + 1
2x = 2y - 7

Here when you substitute in x = y + 1, you get:
2(y+1) = 2y - 7
2y + 2 = 2y - 7
2 = -7 <-- inconsistent system (x or y can be anything and the system will never be true).

So in summary, with your example:
x = -3
y = -6
And since you have a result, the system is independent.

Answer 2

Working in reverse, starting at the top, he descends 7 rungs which is where he finished putting out the fire. He then descended another 7 rungs. Fire flared up. Climbed UP 5 rungs, then descended 3 rungs to the middle rung. So he climbs down 17 rungs but climbs up 5 to get to the middle rung, meaning he climbs down 12 rungs to get to the middle rung. If the 12th rung is the middle rung then there are 11 rungs either side, so there are 23 rungs on the ladder

Answer 3

first equation seems easy so lets go with that
x=3-y
now substitute that into the second one and you get
3(3-y)-2y=3
9-3y-27=3
-3y=3-9+27
y=21/3
y=7
x=3-y
x= -4

dont know about the other stuff

Answer 4

The easiest way is to first solve for one variable and plug it into the other equation.

x-y = 3, solve for y

y = x-3.

Now put this into your other equation:
3x-2y=3 becomes 3x-2(x-3) = 3

3x-2x-3=3
x=6

Now put it back into either equation
x-y=3
6-y=3
y=3

And then you can check your answer by plugging both numbers into both equations.

Answer 5

solve one for y or x.....y=x-3 then put it into the other equation at y.... 3x-2(x-3)=3 and solve.... 3x-2x+6=3..... x+6=3 x=-3.... now go back and put x in the other equation..... y=-3-3 ... y=-6.... as for the dependancy or consistancy i am not sure.

Answer 6

x-y=3
3x-2y=3
equations are independent
x=3+y
3(3+y)-2y=3
9+3y-2y=3
y=3-9=-6
x=3+y=3-6=-3
check
-3-(-6)=-3+6=3

Answer 7

i would say x=3 n y=3

Answer 8

x-y=3 .....1
3x-2y=3.....2
from...1
x=3+y
substituting in ...2
we have
3[3+y]-2y=3
9+3y-2y=3
y=-6
x=-3
verify
3*[-3]-2*[-6]
=-9+12
=3 ok

Answer 9

Why not just email someone all your math homework? Or hey! Pay attention in class and you can do them yourself!