G
Guest
Guest
How do I solve the following system equation:
2x-7y=1
-3xt4y=-8
2x-7y=1
-3xt4y=-8
- Joined
- Feb 4, 2004
- Messages
- 16,582
There are many methods for solving linear systems. Which one(s) are you supposed to use? (Cramer's Rule? matrix row operations? Gauss-Jordan elimination? etc)
When you reply with the method you are using, please also show how far you have gotten in the process. Thank you.
Eliz.
When you reply with the method you are using, please also show how far you have gotten in the process. Thank you.
Eliz.
G
Guest
Guest
The instructions are that I solve each using either the linear combination, substitution or graphing. This is what I have so far:
2x-7y=1
2X - 1 = 7y
2/7(X) - 7 = y
-3X + 4Y = -8
4Y = -8 + 3X
y = 32 + 12X
2x-7y=1
2X - 1 = 7y
2/7(X) - 7 = y
-3X + 4Y = -8
4Y = -8 + 3X
y = 32 + 12X
ABoyd said:
Substitution is a good method for solving a system of equations IF one of the equations can easily be solved for one of the variables WITHOUT introducing fractions. Since that isn't the case here (solving either equation for x or for y will introduce fractions), I'd look at the elimination method.
Note that if you multiply both sides of the first equation by 3, and both sides of the second equation by 2, the x terms will have opposite coefficients, and will add up to 0 if you add the equations together.
First equation multiplied by 3:
6x - 21y = 3
Second equation multiplied by 2:
-6x +8y = -16
Ok...now you've got this:
6x - 21y = 3
-6x +8y = -16
Add the two equations together:
-13y = -13
y = 1
Now, substitute 1 for y in either of the two original equations. I'll use the first one:
2x - 7y = 1
2x - 7(1)= 1
2x - 7 = 1
2x = 8
x = 4
Check. Is the second equation true when x = 4 and y = 1?
-3x + 4y = -8
-3(4) + 4(1) = -8
-12 + 4 = -8
-8 = -8
True. It checks.
I hope this helps you.
G
Guest
Guest
Thank you
Thank you...this really helps.
Thank you...this really helps.