math help!!!=/?

Question

substitution method to solve the linear system

x+3y=9
4x-2y=-6

Answer 1

x+3y=9
4x-2y=-6

x= -3y+9
so
4( -3y+9) -2y=-6
-12y+36-2y=-6
-14y=-42
y=3

x+3(3)=9
x+9=9
x=0

(0,3)

Answer 2

In substitution method what you do is solve one of the equations for one of the variables. Then you plug in the equation into the other one. You can choose to solve for the variable on any of the equations or on any of the variables. The trick is to do it to the one that is most conveniant for you. For example, I know that the bottom equation will result in a fraction. I don't want to deal with that so the top equation becomes more atractive. Also, solving for X on that top equation is also more attractive to me. I mean you can solve for any of them but it is best to make your life easier. So here it is. Solving for X on the top equation.

x + 3y = 9
subtract 3y from both sides
x + 3y -3y = 9 - 3y

x= 9 -3y

alright, now we substitude that equation into the bottom equation for X. In other words, everywhere there is an X in the bottom equation you are going to put in 9 - 3y. Here we go.

4x - 2y = -6 becomes

4(9 - 3y) - 2y = -6

we now simplify (make it prettier) by multiplying that 4 into the 9 and the -3y and we simplify.

(4*9 - 4*3y) - 2y =-6

36 - 12y -2y = -6 simplify more

36 - 10y =-6.

alright, now we can solve for Y since is the only variable left.

-10y = -6 -36

-10y = -42 now we divide by 10

y = -42/-10

y = 21/5 We could get a decimal but then you loose accuracy. fractions are more accurate albeit a pain in the butt to use at times. Life is always about trade offs. Anyways, now that we know what Y is we can substide this known Y value into the first equation and solve for X. In english this means change all the Ys on the first equation for 21/5

x + 3y =9

x + 3(21/5) = 9 multiplying the 3

x + 63/5 = 9 Now solve for X

x = 9 - 63/5 I hate fractions but thats life for you always throwing you a curve ball. We have no choice.

x = 45/5 - 63/5

x = -18/5

alright now we know the two mystery values. X = -18/5 and Y = 21/5

Oh but we are not done yet. I mean we are as far as the problem is concern but that is bad engineering. A good engineer always double checks his work. We don't want that roof to fall on top of all those little kids at chucky cheese now do we!!?? It doesn't matter how bratty they are they are still living human beings and we must respect that. So double check by taking any of the equations and plug in X and Y. You should get the same value on both sides of the equation. I'm tired today so I'm just going to check using the first equation because the math is simpler on that one. You can double check using the bottom equation. It should work on both of them.

x + 3y = 9

-18/5 + 3(21/5) = 9 we multiply the 3.

-18/5 + 63/5 = 9 we now simplify and hopefully the roof won't fall err I mean we should get 9 on both sides of the equation.

45/5 = 9

9 = 9 yayyy!!! chuckee cheese is safe to play at. Unfortunately if the kids keep eating all that junk they will have heart problems when they get older maybe a heart attack by 45. However, that is not our problem, we only get paid to solve the math. Hope this clears things up.

Answer 3

If x+3y=9, then x = 9 - 3y
4x - 2y = -6
4(9 - 3y) -2y = -6
36 -12y -2y = -6
-14y = -42
y = 42/14 = 3
x = 9 - 3y = 9 - 9 = 0

Answer 4

The first answer is x= 3 and y= 2
the second is x= -2 and y= 1.