# simaltaneous equations

• May 12th 2009, 10:03 AM
sello
simaltaneous equations
2x-y=16
3x+2y=17
• May 12th 2009, 10:07 AM
masters
Quote:

Originally Posted by sello
2x-y=16
3x+2y=17

Hi sello,

I assume you need to solve this system. Do you know any techniques? How about 'elimination'? Maybe 'substitution'? Cramer's Rule? Something else? What have you been taught so far?
• May 12th 2009, 12:34 PM
masters
Quote:

Originally Posted by sello

[1] 2x-y=16
[2] 3x+2y=17

Ok, sello,

We'll do this by the 'elimination' method. The idea is to eliminate one of the variables by making them additive inverses of each other and then adding the equations together.

We'll multiply the first equation by 2 and add it to the second equation. This will eliminate the y variable so we can solve for x.

[1] 4x - 2y = 32

[2] 3x + 2y = 17
--------------------
[3] 7x = 49

x = 7

Now substitute this value we found for x into either of the original equations and solve for y. Let's choose [2].

3(7) + 2y = 17

21 + 2y = 17

2y = -4

y = -2

So, the solution to the system is the ordered pair (7, -2)

You can check this by substitution these values for x and y back into each equation to validate.

[1] 4x - 2y = 32

4(7) - 2(-2) = 32

28 + 4 = 32

32 = 32

[2] 3x + 2y = 17

3(7) + 2(-2) = 17

21 - 4 = 17

17 = 17