x+2y=1 2x+y=8    find x and y

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

Let us start by finding a value of y in terms of x.  We will use the second equation and we get:

y = 8 -2x

x + 2 (8 - 2x) = 1

x + 16 - 4x = 1

x - 4x = -15

-3x = -15

x = 5

If x = 5, then we can substitute in...

5 + 2y = 1

2y = -4

y = -2

Now let us check that by substituting those values in to the equation

2x + y = 8

2 (5) + (-2) = 8

That is correct so we have the right values for x and y/

 

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

x+2y=1......(1)

2x+y=8......(2)

We will use the elimination method.

First, multiply (1) by -2 and add to (2)

-2x-4y=-2

2x+y=8

==> -3y=6 ==> y=-2

x+2y=1

==> x= 1-2y = 1-2(-2)= 1+4= 5

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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x + 2y = 1

2x + y = 8   

First multiply everything in the first equation by 2. By multiplying, you should get

2x + 4y = 2

2x + y =   8 now subtract 2x with 2x ( which means subtract 4y with " y " and 2 with 8

By subtracting,  you should get

3y = -6 now divide both sides by 3 

By dividing, you should get 

y = -2   which is your answer for " y " 

Now plug -2 into one of the equation

x + 2 ( -2 ) = 1 multiply 2 with -2

By multiplying, you should get

x - 4 = 1 now add 4 on both sides

By adding, you should get

x = 5.  which is your answer for " x " 

So your answer is x = 5 and y = -2

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

We have two variables, x and y, and following two simultaneous equations>

x + 2y = 1   ...   (1)

2x + y = 8   ...   (2)

We solve these equations for value of x and y as follows.

Multiplying equation (1) by 2 we get:

2x + 4y = 2   ...   (3)

Subtracting equation (2) from equation (3) we get:

2x - 2x + 4y - y = 2 - 8

3y = -6

Therefore:

y = -6/3 = -2

Substituting this value of y in equation (1) we get:

x + (-2*2) = 1

x - 4 = 1

x = 1 + 4 = 5

Answer:

x = 5, y = -2

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve:

x+2y = 1.......... (1) and

2x+y = 8.......... (2)

Solution:

These area pair of simultaneous equations in two variables x and y which could be solved by substittution or elimination methods. Each ofthese methods involves the  idea of reducing the equation to a single variable and then solving for the single variable. Substituting the solution so obtained in any one of the equation, the other unknown is obtained.

This particular type of simultaneous equations have the chararacteristic of the coefficients of x and y in one equation interchange in the other equation. Such equations  could also be solved by adding and subtracting as below:

Add eq(1) and eq(2) and we get: (x+2y)+(2x+y) = 1+8 =9.Or

3(x+y) = 9. Or

x + y = 3.....................................(3).

Suntract (1) from (2): (2x+y) - (x+2y) = 8 - 1 = 7.Or

x - y = 7....................................(4).

Adding eq(3) and eq(4), we get:

2x = 3+7 = 10. So x = 10/2 = 5

Subtracting (4) from (3) , we get:

2y = 3 - (7 ) = -4. Or

y = -4/2 = -2.

So x =5 and y = -2

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