# Solving a linear system by substitution

• Jan 25th 2006, 08:08 AM
josh_c
Solving 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
• Jan 25th 2006, 08:44 AM
SkyWatcher
re hi
i am not sure of what is substitution but here is my guess of what it means
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)
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!
• Jan 25th 2006, 09:19 AM
ticbol
Quote:

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

x-2y=4
2x-3y=7

Substitution here means you express the value of one variable in terms of the other variable from one of the two equations. Say, get x in terms of y, from the 1st equation. Then substitute that into the the 2nd equation, thereby you will have an equation involving only one variable. Blah, blah, blah.

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.
• Jan 25th 2006, 09:21 AM
josh_c
Quote:

Originally Posted by ticbol
Substitution here means you express the value of one variable in terms of the other variable from one of the two equations. Say, get x in terms of y, from the 1st equation. Then substitute that into the the 2nd equation, thereby you will have an equation involving only one variable. Blah, blah, blah.

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.

Thanks i understand now:)