Solve the system x+y-14=0 4x-y-11=0

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve:

x + y - 14 = 0 ...(1)

4x - y - 11 = 0 ...(2)

From (1)

x + y - 14 = 0

=> -y = x - 14

Substitute in (2)

4x + x - 14 - 11 = 0

=> 5x - 25 = 0

=> x = 25/5

=> x = 5

y = 14 - x

=> y = 14 - 5

=> y = 9

The required solution is x = 5 and y = 9

givingiswinning's profile pic

givingiswinning | Student, Grade 10 | (Level 1) Valedictorian

Posted on

x+y-14=0

x = 14 - y

replace y 

4x-y-11=0

subtract 11

4(14 - y) - y = 11

56 - 4y - y = 11

combine like terms

- 4y - y = -56 + 11 

-5y = -45

divide by -5

y = 9

now plug this in as y to get x

x+9-14=0

x - 5=0

add 5

x= 5

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

x+y-14=0

x = 14 - y

now replace y with those numbers in any of the equations:

4x-y-11=0

subtract 11

4(14 - y) - y = 11

56 - 4y - y = 11

combine like therms

- 4y - y = -56 + 11 

-5y = -45

divide by -5

  • y = 9

now plug this in as y to get x

x+9-14=0

x - 5=0

add 5

  • x= 5
giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll re-write the equations, keeping the variables x and y to the left side:

x + y = 14 (1)

4x - y = 11 (2)

We'll solve the system using substitution:

x = 14 - y (3)

We'll replace x in the 2nd equation by the expression from (3):

4(14 - y) - y = 11

We'll remove the brackets:

56 - 4y - y = 11

-5y = 11 - 56

-5y = -45

We'll divide by -5:

y = 9

We'll substitute y in (3):

x = 14 - 9

x = 5

The solution of the system is the pair: (5 ; 9).

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