Apply matrix to solve simultaneous equations x + y - 5 = 0 2x - y -1 = 0

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

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x + y - 5 = 0

==> x + y = 5...........(1)

2x - y - 1 = 0

==> 2x - y = 1.........(2)

We will use the elimination method to solve:

Let us add (1) t0 (2):

==> 2x + x + y - y = 5 + 1

Reduce similar:

==> 3x = 6

Divide by 3:

==> x = 6/3 = 2

==> x = 2

Now to find y , let us substitute in (1):

x + y = 5

2  + y = 5

==> Subtract 2 from both sides:

==> y= 5 - 2 = 3

==> y= 3

Then the solution for the system is the point ( 2,3)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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).

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve the equaations;

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

2x-y-1 = 0....(2).

Adding the equations, we get:

3x-6 = 0

3x= 6.

x = 6/3 = 2.

We substitute x= 2 in eq (2): 2x-y-1 = 0:

2*2 -y -1 = 0

4-y -1 = 0.

Add  y to both sides:

4-1 = y.

So 3 = y.

Therefore x = 2 and y = 3 are the solutions:

Tally :

Put  x= 2 and y = 3 in x+y - 5 = 0 ... (1)and 2x-y-1 = 0...(2)

First equation: LHS 3+2-5 = 0= RHS

Second equation: LHS : 2*2-3-1 = 0 = RHS.

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