Solve the system by using any method. x=53/11-16y/11 x+4y=43

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve for x and y give the equations:

x = 53/11 - 16y/11 ...(1)

x + 4y = 43...(2)

From (1) , we get

=> x = 53/11 - 16y/11

=> 11 x = 53 - 16y

=> 11 x + 16y = 53

Subtract 4*(2) from this

=> 11 x + 16y  - 4x - 16y= 53 - 172

=> 7x = -119

=> x = -119/7

=> x = -17

Substitute x = -17 in (2)

=> -17 + 4y = 43

=> 4y = 60

=> y = 60/4

=> y = 15

Therefore x = -17 and y = 15.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since x is written with respect to y, we'll solve the system using substitution method.

We'll substitute the first equation into the second and we'll get:

53/11-16y/11 + 4y = 43

We'll multiply by 11 the equation:

53 - 16y + 44y = 473

We'll combine like terms:

53 + 28y = 473

We'll subtract 53:

28y = 420

We'll divide by 28:

y = 420/28

y = 15

We'll substitute y = 15 in the first equation of the system:

x = 53/11-16*15/11

x = (53-240)/11

x = -187/11

x = -17

The solution of the system is: {-17 ; 15}.

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