Solve the following system of equations:
x - 2y = 14

x + 3y = 9

Question

Solve the following system of equations:
x - 2y = 14

x + 3y = 9

rebeccaxhawaii · Answer

you need to find x and y coordinates ?

anonymous · Answer

(1, 12)
	(-1, -12)
	(12, -1)
	(12, 1)

whpalmer4 · Answer

$$x -2y = 14$$$$x+3y=9$$
Do you know substitution or combination?

rebeccaxhawaii · Answer

lets do y first and get rid of x

rebeccaxhawaii · Answer

so change all signs for the bottom so therefore -x-3y=-9

anonymous · Answer

ok im not really good  at math

whpalmer4 · Answer

Substitution is easy here as you can quickly get $x$ in terms of $y$ with little work.  Then you plug the expression for $x$ in place of $y$ in the other equation and solve it for the value of $y$.  Once you know $y$, you plug it in to your substitution equation to get $x$.

rebeccaxhawaii · Answer

so both x's cancels out

rebeccaxhawaii · Answer

then you are left with -5y=-5

rebeccaxhawaii · Answer

giving you 1 so y equals one

rebeccaxhawaii · Answer

then replace your answer with y
so x-2(1)=14 then x-2=14

anonymous · Answer

so what would be the answer

anonymous · Answer

its 12 isnt it

rebeccaxhawaii · Answer

wait y would equal -1 sorry

whpalmer4 · Answer

$$x-2y  =14$$$$x-2y+2y = 14 + 2y$$$$x = 14 + 2y$$

Now we take our other equation:
$$x + 3y = 9 $$and replace $x$ with $14+2y$

$$(14+2y) + 3y = 9$$
$$14 + 2y + 3y = 9$$$$14 + 5y = 9$$$$14-14+5y = 9-14$$$$5y = -5$$$$y = -1$$

Now we put our value of $y = -1$ back in the substitution equation to find $x$:

$$x = 14 + 2y $$$$x = 14 + 2(-1)$$$$x = 14 - 2$$$$x = 12$$

Now, the most important step!  Check the work to make sure it solves BOTH equations:

$$x-2y = 14$$$$12-2(-1) = 14$$$$12 + 2 = 14\checkmark$$
$$x+3y=9$$$$12+3(-1) = 9$$$$12 -3  = 9\checkmark$$

rebeccaxhawaii · Answer

so then x-2(-1)=14 then x+2=14 then x=14-2 making x=12

rebeccaxhawaii · Answer

so it would be C

whpalmer4 · Answer

It is entirely possible to get a set of "answers" which only satisfies some of the equations.  For example, x = 0 and y = 3 would work in $$x+3y=9$$ but will not work for $$x-2y=14$$

anonymous · Answer

Solve the system of equations by substitution. What is the solution for x?
2x + y = 1

4x + 2y = -1

anonymous · Answer

i need help

whpalmer4 · Answer

Okay, let's do the same thing.

$$2x+y = 1$$$$4x+2y = -1$$

Can you solve one of those equations to give you 1 variable in terms of the other?  That means get 1 variable all alone on one side of the = sign, everything else on the other.