# 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 (1) by -2 and add to (2):

-2x - 4y = -16

3x + 4y = 16

==> Now add both equations:

==> **x = 0 **

Now to find y , we will substitute with (1):

x + 2y = 8

0 + 2y = 8

==> 2y= 8

**==> y= 4**

**Then, the solution is:**

**(x, y) = ( 0, 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

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 .... (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.**