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
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?
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?
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?