Solve using the addition method. What is the x-value of the solution to the system?

2x – 3y = -1
3x + 4y = 24

Question

Solve using the addition method. What is the x-value of the solution to the system? 

2x – 3y = -1 
3x + 4y = 24

amistre64 · Answer

we can multiply an equation and it keeps its inherent properties intact

amistre64 · Answer

to get rid of the ys, we need to multiply the top and bottom by different values; something such that they will equal the same thing (but opposite)

amistre64 · Answer

or we can go fractiony :)

amistre64 · Answer

2x – 3y = -1   ; /3
3x + 4y = 24  ; /4

2x/3 – 3y/3 = -1/3  
3x/4 + 4y/4 = 24/4 


2x/3 – y = -1/3  
3x/4 + y = 6
---------------
(2/3 + 3/4)x  = 6 - 1/3

$$x=\frac{6-\frac{1}{3}}{\frac23+\frac34}$$

anonymous · Answer

I have no idea what you just did

amistre64 · Answer

lol, um, i divided the top by 3 to make a -y
      i divided the bottom by 4 to make a +y

when you add the 2 resulting equations together, the ys cancel; and you solve for x

amistre64 · Answer

we can do this the same way, but multiply the top by 4 and the bottom by 3

amistre64 · Answer

2x – 3y = -1   ; *4
3x + 4y = 24  ; *3



8x – 12y = -4
9x + 12y = 72
--------------
17x       =  68

amistre64 · Answer

the addition method means that you want to eliminate one of the variables; to do that, you have to multiply (or divide) by some value that turn one of them into opposites

anonymous · Answer

oh okay

anonymous · Answer

I understand that one now. Could you help me with another?

amistre64 · Answer

post it up on the left, and ill see if i can get around to it

anonymous · Answer

Okay thanks :)

amistre64 · Answer

youre welcome :)