Simultaneous equation question?
I can't figure out how to get this second equation into standard form to solve the equations.

x+y=35
18x=24y

I do know that the answer is (20, 15)
can anyone help me with how to solve this?
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answers:
Como say: (4/3) y + y = 35
4 y + 3y = 105
7y = 105
y = 15

x + 15 = 35
x = 20

x = 20 , y = 15
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David say: If x + y = 35 then 24x + 24y = 840 by multiplying all terms by 24
If 18x = 24y then 18x -24y = 0 by subtracting -24 from both sides
Adding both equations together 42x = 840
Dividing both sides by 42: x = 20
So by substitution: x = 20 and y = 15
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lenpol7 say: x + y = 35
18x - 24y = 0 (In standard form)

Multiply the top equation by '24' , and then add. It will remove 'y'
24x + 24 y = 840.
18x - 24y = 0 (In standard form).
42x = 840
Divide by '42'
x = 840/42
x = 20
Substitute this value into either eq'n for 'y'
20 + y = 35
y = 15
or
18(20) = 24 y
360 = 24y
y = 360/24
y = 15.
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Φ² = Φ+1 say: 18x = 24y is (subtracting 24y from both sides) 18x - 24y = 0, which (dividing through by 6) is 3x - 4y = 0

x = (35×-4-1×0)/(1×-4-1×3) = -140/-7 = 20, and y = (1×0-35×3)/(1×-4-1×3) = -105/-7 = 15

I agree that the answer is (20, 15).
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Jeffrey K say: 18x - 24y = 0
Simply subtract 24y from both sides.
You can now solve the simultaneous equations.
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alex say: 18x=24y --->3x=4y --->x = (4y/3)
x+y=35
(4y/3)+y=35
solve for y
then find x
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RR say: (i) x + y = 35
(ii) 18x = 24y

You move the 24y to the left of the equal sign and change signs to negative:
(iii)18x - 24y = 0

You can now multiply (i) by 24 to make y the same as in (iii)
(iv) 24x - 24y = 840

Add (iii) and (iv) together to eliminate y

(v) 42x = 840
x = 20

Substitute x = 20 in (i)
20 + y = 35
y = 15

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or you could rewrite:
18x = 24y
18x/24 = y
3x/4 = y

Substitute into x + y = 35
x + 3x/4 = 35
multiply by 4 to eliminate fraction
4x + 3x = 140
7x = 140
x = 20

Substitute x = 20 in x + y = 35
20 + y = 35
y = 15
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Steve say: 18x = 24y.....so

18x - 24y = 0
24x + 24y = 840
42x = 840
x = 20...etc.
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King Leo say: .

x + y = 35

18x = 24y
∴ y = ¾x

x + y = 35
x + ¾x = 35
4x + 3x = 140
7x = 140
7x/7 = 140/7
∴ x = 20

y = ¾x
y = ¾(20)
y = 15

( 20, 15 )
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Alan say: see image
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khalil say: x+y=35
18x=24y
make the coefficients x or y equal but opposite signs.
i choose x ....so ..multiply the first by -18
-18x - 18y = -630
18x = 24y
now add together
-18y = -630 + 24y
tranfer 24y to the left with changing its sign (this is a rule)
-18y -24y = -630
-42y = -630
y = 15 ◄◄◄
and from the first
x = 35 - 15 = 20 ◄◄◄
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Ash say: Just move the 24y to left side
18x - 24y = 0
6(3x - 4y) = 0
divide by 6 on both sides
3x - 4y = 0 ...(2)

Now multiply the 1st equation by 4
4x + 4y = 140
Add it to (2)
3x - 4y + (4x + 4y) = 0 + 140
7x = 140
x = 20
plug in first equation
20 + y = 35
y = 15

(20, 15)
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