Solve for x and y using x + 2y = 8 and 3x + 4y = 16
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x+ 2y = 8........(1)
3x + 4y = 16........(2)
Let us use the elimination method to solve:
We'll multiply...
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The set of equations x + 2y = 8 and 3x + 4y = 16 has to be solved for the variables x and y.
From the equation x + 2y = 8, write x = 8 - 2y
Now substitute for x in the equation 3x + 4y = 16
3*(8 - 2y) + 4y = 16
24 - 6y + 4y = 16
-2y = -8
y = 4
x = 8 - 2y = 8 - 8 = 0
The solution of the set of equations is x = 0 and y = 4
x + 2y = 8
3x + 4y = 16
Multiply, the everything in the first equation by 3
By multiplying, your equation should look like
3x + 6y = 24
3x + 4y = 16 now, subtract 3x with 3x ( also subtract 6y with 4y and 24 with 16)
By subtracting your equation should look like
2y = 8 divide both sides by 2
By dividing, your equation should look like
y = 4 which is your answer for " y "
Now plug 4 into one of the equation
x + 2 ( 4 ) = 8 multiply 2 with 4
By multiplying, your equation should look like
x + 8 = 8 subtract 8 on both sides
By subtracting, your equation should look like
x = 0 which is your answer for " x "
So, your answer is x = 0 ; y = 4
(a) x + 2y = 8
(b) 3x + 4y = 16
I'm going to use the method called elimination.
First multiply (a) by 2:
2x + 4y = 16
Subtract this from b:
3x + 4y = 16
- 2x + 4y = 16
---------------------
x = 0
Rearrange (a) to solve for y:
x + 2y = 8
y = ( 8 - x)/2
Plug in our known value of x:
y = ( 8 - 0) / 2
y = 4
So x = 0 and y = 4
x+2y=8
x+2y-2y=8-2y
x=8-2y
3x+4y=16
3(8-2y)+4y=16
24-6y+4y=16
24-6y+4y-24=16-24
-6y+4y=-8
-2y=-8
-2y/-2=-8/-2
y=4
x+2(4)=8
x+8=8
x+8-8=8-8
x=0
So the answer for x=0 and y=4
x+2y = 8 .... (1).
3x+4y = 16..(2).
From (1) : 2y = 8-x. Or y = (8-x)/2.
We put y = (8-x)/2 in the second eq: 3x+y = 16.
3x+4(8-x)/2 = 16.
Multoiply by 2:
6x+4(8-x) = 2*16 = 32.
6x+32-4x = 32
6x-4x = 32-32 = 0
2x = 0
x = 0.
Put x= 0 in first equation x+2y = 8.
0+2y = 8
2y = 8
y = 8/2 = 4.
Therefore x = 0 and y = 4 are the solutions.
We have the equations
x + 2y = 8 … (1)
3x + 4y = 16… (2)
Now we have to use (1) and (2) to find the value of x and y.
First use (2) – 2*(1)
=> 3x + 4y – 2*( x + 2y) = 16 – 2*8
=> 3x + 4y – 2x – 4y = 16 – 16 = 0
=> x = 0
Substitute x = 0 in (1)
=> 0 + 2y = 8
=> y = 8/2
=> y = 4
Therefore x = 0 and y = 4
The required solution is x = 0 and y = 4.
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