Solve the following equations algebraically

2x + y = 0

−2x −3y = 8 im stuck i can do the easy ones when in the format y=mx+c

Printable View

- Sep 11th 2009, 08:42 PMrealisticsim equations
Solve the following equations algebraically

2x + y = 0

−2x −3y = 8 im stuck i can do the easy ones when in the format y=mx+c - Sep 11th 2009, 08:47 PMVonNemo19
Thee's generally two ways to do these, but I'll hint towards the addition method because it is alreaddy set up

Add the two equations like term by like term

$\displaystyle 2x+(-2x)=0$

$\displaystyle y+(-3y)=-2y$

$\displaystyle 0+8=8$

Now set up what's left

$\displaystyle -2y=8$

Can you finish? - Sep 11th 2009, 08:49 PMrealistic
- Sep 11th 2009, 08:57 PMVonNemo19
It's called the substitution method.

EG

We have the sim equations

$\displaystyle x+y=1$ and $\displaystyle 3x-2y=7$

Then we solve for a variable in one of the equations and substitute for the variable in the other

$\displaystyle x+y=1$

$\displaystyle y=1-x$

Now we sub for y in the other

$\displaystyle 3x-2\overbrace{(1-x)}^y=7$

solve for x and we can determine the solution

$\displaystyle 3x-2(1-x)=7$

$\displaystyle 3x-2+2x=7$

$\displaystyle 5x=9$

$\displaystyle x=\frac{9}{5}$

Now we put $\displaystyle \frac{9}{5}$ back in the original for x.

Do you see? - Sep 11th 2009, 09:00 PMrealistic
- Sep 11th 2009, 09:06 PMVonNemo19
- Sep 11th 2009, 09:13 PMrealistic
- Sep 11th 2009, 09:24 PMVonNemo19
Think of it like a game, with the object being to line thx's and y's up underneath of each other and then add or subtract them to get rid of one of them.

$\displaystyle 2x = 11-3y$

$\displaystyle 0= 6x-2y+11$

You can see here that the x's and y's are not right underneath of each other, but wait...

$\displaystyle 2x =-3y+11$

$\displaystyle -6x=-2y+11$

Now the x's and y's are lined up. But remember that the object is to add (or subtract) so that I eliminate one of the variables. To do this I have to do a little trick with multiplication...

$\displaystyle (-3)(2x) =(-3y+11)(-3)$

$\displaystyle -6x=-2y+11$

$\displaystyle -6x =9y-33$

$\displaystyle -6x=-2y+11$

Now look! The x's and y's are still lined up, but now if I subtract the two equations, the x's will dissapear and I can solve for y!

Do you see? - Sep 11th 2009, 09:29 PMrealistic
- Sep 11th 2009, 09:31 PMVonNemo19
- Sep 11th 2009, 11:28 PMrealistic
been doing alot of them and just got stuck at this one

3y +2x +10 = 0

2y = x −2

=

3y +2x +10 = 0

2y - x +2 = 0

x by 2? then add both? i tried but got wrong answer (Headbang) - Sep 12th 2009, 05:27 AMVonNemo19
- Sep 12th 2009, 05:56 AMrealistic
- Sep 12th 2009, 06:00 AMMatt Westwood
Add them, don't subtract them.

- Sep 12th 2009, 06:02 AMrealistic