SystemSolve the system 2x+3y=8 x+8y=17

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

Find matrix of system (2  3)

                                (1  8)

You need to evaluate deerminant of matrix such that:

Det A = 16 - 3 = 13

You need to find x such that:

x = Det x/Det

 You need to form determinant Det x such that:

(8   3) => Det x = 64 - 51 => Det x = 13

(17  8)

x = 13/13 => x = 1

Since y = Det y /Det, you need to evaluate Det y such that:

Det y = 2*17 - 8 = 34 - 8 => Det y = 26

y = 26/13 => y = 2

Hence, the solution to the system is (1,2).

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve:

2x+3y=8 ...(1)

x+8y=17 ...(2)

x + 8y = 17

=> x = 17 - 8y

substitute in (1)

2(17 - 8y) + 3y = 8

=> 34 - 16y + 3y = 8

=> -13y = -26

=> y = 2

x = 17 - 16 = 1

The solution is (1 , 2)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll solve the system of equations using the elimination method, also:

2x+3y= 8 (1)

x+8y= 17 (2)

We'll multiply (2) by -2:

-2x - 16y = -34 (3)

We'll add (3) to (1):

2x + 3y - 2x - 16y = 8 - 34

We'll combine like terms:

-13y = -26

We'll divide by -13 both sides:

y = 2

We'll substitute y = 2 in (2):

x+8y= 17

x + 16 = 17

We'll subtract 16 both sides:

x = 17 - 16

x = 1

The solution of the given system is {(1 , 2)}.

We could also use the substitution method. We'll write x with respect to y, from the equation (2).

x+8y= 17

x = 17 - 8y (3)

We'll substitute x in (1):

2(17 - 8y)+3y= 8

We'll remove the brackets:

34 - 16y + 3y = 8

We'll combine like terms:

-13y = 8 - 34

-13y = -26

We'll divide by -13:

y = 2

We'll substitute y in (3):

x = 17 - 16

x = 1

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