Question 22321: 3x+2y=4
4x-5y=4
I have to solve to get an x and a y and i'm totally confused about how to go about it. I'm trying to help a friend and explain it but i forget how to do these equations.
Thank you for your help
Answer by MORUPHOSUOLALE(24)  (Show Source):
You can put this solution on YOUR website! SOLUTION
THIS IS A SIMULTANEOUS EQUATION.
YOU CAN EITHER SOLVE IT BY ELIMINATION METHOD OR SUBSTITUTION METHOD.
ELIMINATION METHOD HAS BEEN THE EASIEST AND FAST METHOD OF SOLVING ANY SIMULTANEOUS EQUATION.
LET'S SEE:BY ELIMINATION METHOD.
3X+2Y=4 --eq 1
4X-5Y=4 --eq 2
STEP 1
MULTIPLY EQUATION ONE BY 4 THROUGHOUT AND SIMULTANEOUSLY MULTIPLY EQUATION TWO BY 3 THROUGHOUT.( 3 WAS DERIVE FROM CO-EFFICIENT OF X IN EQUATION ONE AND 4 WAS DERIVE FROM CO-EFFICIENT OF X IN EQUATION TWO,THIS IS TRUE ALL THE TIME FOR ANY SIMULATENEOUS EQUATION USING ELIMINATION METHOD APPROACH.
THOSE EQUATION WILL BECOME
12X+8Y=16 --EQ 3
12X-15Y=12--EQ 4
STEP TWO- SUBTRACT EQUATION 4 FROM EQUATION THREE
23Y=4
Y=4/23
TO GET THE VALUE OF X.
PLUG IN 4/23 FOR Y ,IN ANY OF THE EQUATION TO GET X.
3X+2Y=4 -EQ 1
3X+2(4/23]=4
3x+8/23=4
3x=4-(8/23)(by collecting like terms}
3x=(92-8}/23
3x=84/23
x={84/23}X (1/3}
X=28/23
we can always check if we are right by proof evaluattion.
by plugging both values of x and y in any of the equation respectively if we do so the left hand side must eqaul to the right hand side to certify that we are right.
let'see-
by taking any equation,say equation one.
3x+2Y=4
3{28/23)+2(4/23)=4
(84/23)+(8/23}=4
3.65 + 0.35 =4
This tells us our value of x and y are correct,this proof is true at all time to proof or check any given value of x and y,in any simulataneous equation problems.
Thank you.
Moruph Osuolale
mosuolal@uncc.edu
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