# System of linear equations.

• Aug 9th 2010, 07:22 PM
gabriel
System of linear equations.
how do i solve for this system of equations

11x-3y=-36
12y-9x=39
?
tried reordering the terms but what else?
• Aug 9th 2010, 07:51 PM
pickslides
Quote:

Originally Posted by gabriel
how do i solve for this system of equations

11x-3y=-36
12y-9x=39
?
tried reordering the terms but what else?

$\displaystyle 11x-3y=-36$ ...(1)
$\displaystyle 12y-9x=39$ ...(2)

From (1) $\displaystyle 11x-3y=-36\implies -3y=-36-11x \implies y=12+\frac{11}{3}x$

Then (2) $\displaystyle 12y-9x=39\implies 12\left(12+\frac{11}{3}x\right)-9x=39$ Can you finish it from here?
• Aug 9th 2010, 08:08 PM
gabriel
yeppp i got thnx good refreshment to the dusty mind
• Aug 9th 2010, 10:14 PM
Prove It
Quote:

Originally Posted by gabriel
how do i solve for this system of equations

11x-3y=-36
12y-9x=39
?
tried reordering the terms but what else?

The alternative method (the method used for more equations with more unknowns) is the elimination method...

$\displaystyle 11x - 3y = -36$
$\displaystyle -9x + 12y = 39$.

Multiply the first equation by 4 to give

$\displaystyle 44x-12y=-144$
$\displaystyle -9x+12y=39$

Add the equations together

$\displaystyle (44x-12y)+(-9x+12y)=-144+39$

$\displaystyle 35x=-105$

$\displaystyle x = -3$.

Substitute into one of the original equations...

$\displaystyle 11(- 3) - 3y = -36$

$\displaystyle -33- 3y = -36$

$\displaystyle -3y = -3$

$\displaystyle y = 1$

So the solution is $\displaystyle (x,y) = (-3,1)$.
• Aug 9th 2010, 10:39 PM
earboth
Quote:

Originally Posted by Prove It
...

$\displaystyle (44x-12y)+(-9x+12y)=-144+39$

$\displaystyle 35x=105$ <=== unfortunately you made a small sign mistake here

$\displaystyle x = 3$.

Substitute into one of the original equations...

$\displaystyle 11\cdot 3 - 3y = -36$

$\displaystyle 33- 3y = -36$

$\displaystyle -3y = -69$

$\displaystyle y = 23$.

So the solution is $\displaystyle (x,y) = (3,23)$.

$\displaystyle (44x-12y)+(-9x+12y)=-144+39$

$\displaystyle 35x=-105$

$\displaystyle x = -3$.
• Aug 9th 2010, 11:03 PM
Prove It
Yes I did, edited :)