SOLUTION: solving sytems of equations using elimination and my promblem is x+y=4.4 2x+y=3.8

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Question 1008528: solving sytems of equations using elimination and my promblem
is x+y=4.4
2x+y=3.8
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=4.4
2x%2By=3.8
----------------------
Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


Lets start with the given system of linear equations

1%2Ax%2B1%2Ay=4.4
2%2Ax%2B1%2Ay=3.8

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 1 and 2 to some equal number, we could try to get them to the LCM.

Since the LCM of 1 and 2 is 2, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -1 like this:

2%2A%281%2Ax%2B1%2Ay%29=%284.4%29%2A2 Multiply the top equation (both sides) by 2
-1%2A%282%2Ax%2B1%2Ay%29=%283.8%29%2A-1 Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
2%2Ax%2B2%2Ay=8.8
-2%2Ax-1%2Ay=-3.8

Notice how 2 and -2 add to zero (ie 2%2B-2=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%282%2Ax-2%2Ax%29%2B%282%2Ay-1%2Ay%29=8.8-3.8

%282-2%29%2Ax%2B%282-1%29y=8.8-3.8

cross%282%2B-2%29%2Ax%2B%282-1%29%2Ay=8.8-3.8 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.



So after adding and canceling out the x terms we're left with:

1%2Ay=5

y=5 Divide both sides by 1 to solve for y



y=5 Reduce


Now plug this answer into the top equation 1%2Ax%2B1%2Ay=4.4 to solve for x

1%2Ax%2B1%285%29=4.4 Plug in y=5


1%2Ax%2B5=4.4 Multiply



1%2Ax=4.4-5 Subtract 5 from both sides

1%2Ax=-0.600000000000001 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ax=%28-0.600000000000001%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.


x=-0.600000000000001 Multiply the terms on the right side


So our answer is

x=-0.600000000000001, y=5

which also looks like

(-0.600000000000001, 5)

Notice if we graph the equations (if you need help with graphing, check out this solver)

1%2Ax%2B1%2Ay=4.4
2%2Ax%2B1%2Ay=3.8

we get



graph of 1%2Ax%2B1%2Ay=4.4 (red) 2%2Ax%2B1%2Ay=3.8 (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).


and we can see that the two equations intersect at (-0.600000000000001,5). This verifies our answer.



you can also round it to x=-0.6+
so, solutions are:
x=-0.6+
y=5

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
solving sytems of equations using elimination and my promblem
is x+y=4.4
2x+y=3.8
 x + y = 4.4 ------- eq (i)

2x + y = 3.8 ------- eq (ii)



Procedure:

1)  Subtract eq (ii) from eq (i) to ELIMINATE y and determine the value of x

2)  Substitute the value for x in either eq (i) or (ii) to get the value of y.

That's it: Nothing more to it!