SOLUTION: solve each system by substitution 1)4y=3x+6 2x-3y=-5 2)5x-3y=1 2x-3y=-5

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Question 167383: solve each system by substitution
1)4y=3x+6
2x-3y=-5
2)5x-3y=1
2x-3y=-5
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
1)4y=3x%2B6------------> EQN 1
2x-3y=-5 ------------> EQN 2
On EQN 1,
4y=3x%2B6 ---> cross%284%29y%2Fcross%284%29=%283x%2B6%29%2F4
y=%283%2F4%29%28x%29%2B%286%2F4%29, reduced ----> y=%283%2F4%29x%2B%283%2F2%29--> Subst. in EQN 2
2x-3%28%283%2F4%29x%2B%283%2F2%29%29=-5
2x-%289%2F4%29x-%289%2F2%29=-5
%288x-9x%29%2F4=-5%2B%289%2F2%29, combine similar terms, add/subtract
%28-1x%2F4%29=%28-10%2B9%29%2F2
%28-1%2F4%29x=%28-1%2F2%29 --> cross%28-1%2F4%29x%2Fcross%28-1%2F4%29=%28-1%2F2%29%2F%28-1%2F4%29
x=%28-1%2Fcross%282%291%29%28cross%28-4%292%2F1%29
highlight%28x=2%29
Via EQn 1: 4y=3%282%29%2B6
cross%284%29y%2Fcross%284%29=%286%2B6%29%2F4=12%2F4=3 --> highlight%28y=3%29
Check via EQN 1:
4%283%29=3%282%29%2B6
12=6%2B6
12=12, good
.
2)5x-3y=1 ----------> EQN 3
2x-3y=-5 -----------> EQN 4
On EQN 3:
5x=3y%2B1 ----> cross%285%29x%2Fcross%285%29=%283y%2B1%29%2F5
x=%283%2F5%29y%2B%281%2F5%29 ---> subst. in EQN 4
2%28%283%2F5%29%28y%29%2B%281%2F5%29%29-3y=-5
%286%2F5%29y%2B%282%2F5%29-3y=-5, combine similar terms
%282%2F5%29%2B5=3y-%286y%2F5%29
%282%2B25%29%2F5=%2815y-6y%29%2F5
27%2F5=9y%2F5
cross%289%2F5%29y%2Fcross%289%2F5%29=%2827%2F5%29%2F%289%2F5%29
y=%2827%2Fcross%285%29%29%28cross%285%29%2F9%29=highlight%2827%2F9=3=y%29
Via EQN 3:

highlight%28x=2%29
check Via EQN 4:
2%282%29-3%2827%2F9%29=-5
4-cross%283%291%2827%2Fcross%289%293%29=-5
4-9=-5
-5=-5, good
Thank you,
Jojo