Question 149514: How do I solve the following system of linear equation
4x - 3y = 9
2x + y = 12
Answer by tryin2bhelpful(6)   (Show Source):
You can put this solution on YOUR website! Systems are really simple, sometimes people let them get the best of them...
What you want to do is make a variable in one equation, cancel out the same variable in the other equation
For example... y and -y, 2x and -2x, 3z and -3z
But remember! what you do to one variable, you have to do to the WHOLE equation...
With this equation, let's pick 2x and 4x...
We're going to multiply the 2x+y=12 equation by (-2) so that 2x becomes the OPPOSITE of 4x...
Like this...
(2x+y=12)*(-2)
-4x-2y=-24
now, we can add the other equation to it...
-4x-2y=-24
+ 4x-3y= 9
_____________
-5y= -15
Divide both sides by "-5"
y= 3
Now you subsitute 3 for y in the original problem.
2x + y = 12
2x + (3)= 12
Subtract 3 from both sides
2x + 3 (-3) = 12 (-3)
2x= 9
x= 9/2
Now you've solved the system!! Good luck!
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