:confused: i have to solve this by substitution and then check it and im not sure how?

x-2y=4

2x-3y=7

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- January 25th 2006, 09:08 AMjosh_cSolving a linear system by substitution
:confused: i have to solve this by substitution and then check it and im not sure how?

x-2y=4

2x-3y=7 - January 25th 2006, 09:44 AMSkyWatcher
re hi

i am not sure of what is substitution but here is my guess of what it means

you've got your first equation

ax+by=c (general case ) it could be write as ax-c=-by

so y=(c-ax)/a (you should be familiar with that sort of manipulation, check a is non null)

so in your second equation

you replace the y by the expression find above in the second equation you should get an equation of the form ax=b (when compacted) so you know how to find x (if a is null then b must be null or no solution) then you find y using the expression you where ... using!

no needs to say that you must check you allway does in math, twice or more is beter

re By! - January 25th 2006, 10:19 AMticbolQuote:

Originally Posted by**josh_c**

From the 1st equation, we get the value of x in terms of y,

x -2y = 4 ------(1)

x = 2y +4 ------(1a)

Then we substitute that into the 2nd equation,

2x -3y = 7 -----------(2)

2(2y +4) -3y = 7

4y +8 -3y = 7

4y -3y = 7 -8

y = -1 ---------***

Substitute that into, say, (1a), ----[you can substitute that into any of the (1), (1a), or (2) equations above.]

x = 2(-1) +4

x = -2 +4

x = 2 -----------***

Check those findings against the original equations (1) and (2),

x -2y = 4 --------(1)

2 -2(-1) =? 4

2 +2 =? 4

4 =? 4

Yes, so, OK.

2x -3y = 7 -----------(2)

2(2) -3(-1) = 7

4 +3 =? 7

7 =? 7

Yes, so, OK.

Therefore, x=2 and y = -1. -----------answer. - January 25th 2006, 10:21 AMjosh_cQuote:

Originally Posted by**ticbol**