solving systems of linear equ. - substitution or addition

[van]

equ #1) 7x + 4y = 69.21
equ #2) 11x + 2y = 40.23


(4y)/4 = (69.21 -7x)/4
y = 17.30 - 1 3/4 x

11x + 2(17.30 - 1 3/4 x) = 40.23
11x + 34.60 - 3 1/2 = 40.23
11x + 31.10 = 40.23
11x = 9.13
x = .83

7(.83) + 4y = 69.21
5.81 + 4y = 69.21
4y = 63.40
y = 15.85

so, i guess that i have solved for x and y, but when i check back it doesn't work out. can anyone spot where i messed up?

 

[Mrspi]

Re: solving systems of linear equ. - substitution or additio

equ #1) 7x + 4y = 69.21
equ #2) 11x + 2y = 40.23


(4y)/4 = (69.21 -7x)/4
y = 17.30 - 1 3/4 x

11x + 2(17.30 - 1 3/4 x) = 40.23
11x + 34.60 - 3 1/2 = 40.23
11x + 31.10 = 40.23
11x = 9.13
x = .83

7(.83) + 4y = 69.21
5.81 + 4y = 69.21
4y = 63.40
y = 15.85

so, i guess that i have solved for x and y, but when i check back it doesn't work out. can anyone spot where i messed up?

Substitution is not really a very convenient method to use to solve this system (as you've discovered) because neither of the equations can be solved for either variable without introducing fractions.

Since your subject line says "substitution or addition," I'd suggest using the addition method.

Notice that if you multiply both sides of the second equation by -2, the coefficients of the y-terms will be opposites. Then, if you add the two equations together, you'll eliminate the y variable.

Multiply both sides of the second equation by -2:

-2(11x + 2y) = -2(40.23)
-22x - 4y = -80.46

Now....your system looks like this:

7x + 4y = 69.21
-22x - 4y = -80.46
---------------------
-15x + 0y = -11.25

-15x = -11.25

Dividing both sides by -15 gives us this:

x = 0.75

Now...you finish. Pick one of the original equations. Substitute 0.75 for x....and solve for y.

Check to make sure both equations are true for the values you've got for x and y.

 

[Denis]

Re: solving systems of linear equ. - substitution or additio

equ #1) 7x + 4y = 69.21
equ #2) 11x + 2y = 40.23

Suggestion:
700x + 400y = 6921
1100x + 200y = 4023
Get my drift?

 

[Mrspi]

Re: solving systems of linear equ. - substitution or additio

equ #1) 7x + 4y = 69.21
equ #2) 11x + 2y = 40.23

Suggestion:
700x + 400y = 6921
1100x + 200y = 4023
Get my drift?

Not really, Denis...can you be a bit more specific?

MrsPi
Janet

 

[galactus]

Denis got rid of the decimals. The suggestion is that it's easier to work with integers.

 

[Denis]

Thanks galactus. Janet, t'was meant for the poster....as a suggestion.