Algebraic methods: the elimination method?

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princess

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Can anyone please help me solve this question, I've been having trouble trying to figure it out.

Solve the system of equations using the elimination method:
3x + 4y = 8.10 (1)
x +3y = 4.20 (2)

Thanks.
 
In eqtn (2) x = 4.20 - 3y

Substitute (Plug) this value of x into eqtn (1) ... 3( 4.20 - 3y ) + 4y = 8.10

Expand and solve for y

Then substitute this value of y into eqtn (2) to get the value of x
 
well you do the 2nd equation times by 3 (so you can cancel the x's and leave y-it will make sense soon)
to leave:y=3.90
then if you substiute this back into the first equation it will be
3x+15.6=8.10
then -15.6 from both sides
so it is 3x=-7.5
divide by 3 on both sides
to leave x=-2.5
then simply check
but i assure you that you will find i am right
 
3x + 4y = 8.10 --------------(1)
x +3y = 4.20 ---------------(2)
multiply 2nd eqn by -3 and add , to get
(3x + 4y ) - (3x - 9y) = (8.1) - 12.6
=> - 5y = - 4.5
=> y = 4.5 / 5 = 0.9
put this in Eqn (2), to get
=> x + 3(0.9) = 4.2
=> x = 4.2 - 2.7 = 1.5
so x = 1.5 ; y = 0.9
Answer
Is it correct?
 
You have to pick either the x's or y's and make them equal to eachother. It's kinda like trying to add and subtract fractions. You need to multiply the whole equation by a number on both sides and then multiply the second by the other number that makes either the x's or y's equal in both equations.

So, you can multiply to first equation by 3 on both sides and the second by 4 on both sides

OR

Just multiply the second by 3 on both sides to make the X's equal.

I hope this makes sense! :D
 
I would multiply the second equation by -3 and add to the first, thereby eliminating the x-variables.

3x + 4y = 8.10
-3x - 9y = -12.60

-5y = -4.50
y = 0.90

x + 2.70 = 7.20
x = 4.50

(4.50, 0.90)
 
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