Accepted Answer

Sure, here you go!

 

Solve the system of linear equations

3x - 4y = 11
-3x + 2y = -7

 

Now I encourage you to try and solve this, and show your work and explanation.

Can you solve this by the Substitution Method? If so, show how.

Add 3x to the second equation:
2y = -7 + 3x

Divide by 2:
y = -7/2 + 3x/2

 

Plug that into the first equation:
3x - 4(-7/2 + 3x/2) = 11

Simplify:
3x + 14 - 6x = 11
-3x + 14 = 11
Subtract 14:
-3x = -3
Divide by -3:
x = 1

Get y:
y = -7/2 + 3*1/2
Simplify:
= -7/2 + 3/2
= -4/2
= -2

So: (1, -2)

 

 

Can you solve this by the Addition Method? If so, show how.
Add the two equations:
3x - 4y - 3x + 2y = 11 - 7
Simplify:
-2y = 4
Divide by -2:
y = -2

Get x:
3x - 4(-2) = 11
Simplify:
3x + 8 = 11
3x = 3
x = 1

So: (1, -2)

 

Which method do you feel was easier to implement for this problem (Substitution or Addition)?

The addition method is MUCH easier, since the 3x and -3x cancel each other out when you add up the two equations. You don't have to deal with fractions.

 

PS: If you really want to challenge yourself, solve the following system of equations:

2x = 7y - 17
5y = 17 - 3x

Multiply the first equation by 3/2:
3x = 21y/2 - 51/2

 

Plug that into the second equation for 3x:
5y = 17 - (21y/2 - 51/2)

Simplify:
5y = 17 - 21y/2 + 51/2
5y = 85/2 - 21y/2

Add 21y/2:
85/2 = 31y/2
Multiply by 2:
85 = 31y
Divide by 31:
y = 85/31

Get x:
3x = 21y/2 - 51/2
Divide by 3:
x = 7y/2 - 17/2

 

Plug in y:
x = 7*(85/31)/2 - 17/2
Simplify:
x = (595/31)/2 - 17/2
x = (68/31)/2
= 34/31

Making the answer:
(34/31, 85/31)

Let me know if you have any questions,
Scott

Expert:	Scott
Pos. Feedback:	100.0 %
Accepts:
Answered:	1/6/2009

MIT Graduate

College degree in math... proficient in all levels -- from algebra to calculus