SOLUTION: please solve 4x-12y=16 8x+4y=24

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Question 200992: please solve 4x-12y=16
8x+4y=24
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given:system%284x-12y=16%28red%28EQN1%29%29%2C8x%2B4y=24%28red%28EQN2%29%29%29

Multiply red%28EQN2%29 by 3 then add to red%28EQN1%29:
(8x%2B4y=24%28red%28EQN2%29%29)(3)
red%2824x%2B12y=72%29

4x-cross%2812y%29=16%28red%28EQN1%29%29
+red%2824x%2Bcross%2812y%29=72%29
----------------------------
28x=88 ---> cross%2828%29x%2Fcross%2828%29=88%2F28=22%2F7
highlight%28red%28x=22%2F7%29%29, subst. in red%28EQN1%29

4%28highlight%2822%2F7%29%29-12y=16
88%2F7-16=12y
%2888-112%29%2F7=12y ----> -24%2F7=12y ----> %28-24%2F7%29%2F12=cross%2812%29y%2Fcross%2812%29
y=%28-24%2F7%2A12%29=-24%2F84, divide both by 12
highlight%28red%28y=-2%2F7%29%29

*These two lines meet at point (22/7,-2/7) or (3.14,-0.2857)

In red%28EQN1%29, let Fy=0:
4x-12y=16
4x-12%280%29=16 ---> 4x=16 --->cross%284%29x%2Fcross%284%29=cross%2816%294%2Fcross%284%29
x=4, X-Intercept
Let fx=0:
4%280%29-12y=16
-12y=16 ---> y=16%2F-12
y=-4%2F3, Y-Intercept


In red%28EQN2%29, let Fy=0:
8x%2B4y=24
8x%2B4%280%29=24 ---> cross%288%29x%2Fcross%288%29=cross%2824%293%2Fcross%288%29
x=3, X-Intercept
let Fx=0:
8%280%29%2B4y=24 ---> cross%284%29y%2Fcross%284%29=cross%2824%296%2Fcross%284%29
y=6, Y-Intercept




Thank you,
Jojo