Simultaneous equations x + y - 5 = 0 2x - y -1 = 0

4 Answers | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to solve for x and y the system of simultaneous equations, hence, you may use elimination method, such that:

`{(x + y = 5),(2x - y = 1):} => x + y + 2x - y = 5 + 1`

Reducing duplicate members yields:

`3x = 6 => x = 2`

Replacing 2 for x in any of two equations yields:

`2 + y = 5 => y = 5 - 2 => y = 3`

Hence, evaluating the system of simultaneous equations, using elimination method, yields `x = 2, y = 3.`

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll re-write the equations:

x + y = 5

2x - y = 1

We'll use the matrix to solve the system. We'll form the matrix of the system, using the coefficients of x and y:

[1        1]

A =

[2       -1]

We'll calculate the determinant of the system:

detA = -1 - 2 = -3

Since det A is not zero, the system is determinated and it will have only one solution.

x = det X/detA

|5        1|

det X =

|1       -1|

detX = -5 - 1 = -6

x = det X/detA

x = -6/-3

x = 2

We'll calculate y:

|1        5|

det Y =

|2       1|

det Y = 1 - 10

det Y = -9

y = detY/detA

y = -9/-3

y = 3

The solution of the system is: (2 , 3).

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The set of equations x + y - 5 = 0 and 2x - y -1 = 0 has to be solved.

From x + y - 5 = 0 we can express x in terms of y as x = 5 - y

Substitute for x in 2x - y - 1 = 0

2(5 - y) - y - 1 = 0

10 - 2y - y - 1 = 0

-3y = -9

y = 3

x = 5 - y = 5 - 3 = 2

The solution of the given system of equations is x = 2 and y = 3

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on



(1) x + y - 5 = 0
(2) 2x - y - 1 = 0

Add eq (1) and eq (2)
3x - 6 = 0

Now its a single variable problem and you can solve for x. Plug this value back into one of the original equations and solve for y.



We’ve answered 318,918 questions. We can answer yours, too.

Ask a question