Solve the following equations: x + 8y = 19 and 3x - y = 4

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The set of linear equations

x + 8y = 19 ...(1)

3x - y = 4 ...(2)

has to be solved for x and y

From (1)

x = 19 - 8y

Substitute in (2)

=> 3(19 - 8y) - y = 4

=> 57 - 24y - y = 4

=> 53 = 25y

=> y = 53/25

x = 51/25

The solution of the set of equations is x = 51/25, y = 53/25

malagala's profile pic

malagala | College Teacher | (Level 2) Adjunct Educator

Posted on

X + 8Y = 19   ...(1)

3X - Y = 4      ...(2)

 

multiply the second equation by 8

8 x (2) => 24X - 8Y = 32 ....(3)

 

add the first and third equations

(1)+(3)=> X + 8Y +24X -8Y = 19 + 32

           =>   25X =51

           => X = 51/25 

Substitute this value in the  second equation

=> 3X - Y = 4

=>3 (51/25) - Y = 4

=> Y = 3(51/25) -4 

=> Y = (153/25) - 4

=> Y = (153/25) - (100/25)

=>Y = 53/25

 

 

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

x  + 8y = 19

3x -  y  = 4

First, multiply everything in the first equation by 3

By multiplying, your equation should look like

3x + 24y = 57

3x  -   y    = 4  now, subtract 3x with 3x ( which means subtract 24y with " y " and 57 with 4 )

By subtracting, your equation should look like

25y = 53 now divide both sides by 25

By dividing, your equation should look like

y = 53/25 which is your answer for  " y "

Now, plug 53/25 into one of the equation

3x -  53/25  = 4 add 53/25 on both sides

By adding, your equation should look like

3x = 153/25 now divide both sides by 3

By dividing, your equation should look like

x = 51/25 which is your answer for " x "

So your answer is x = 51/25     ;    y = 53/25

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

(a) x + 8y = 19
(b) 3x - y = 4

1. (c) = Multiply (b) by 8: 
24x - 8y = 32

2. Add (a) and (c)

     24x - 8y = 32
+
     x    + 8y = 19
-------------------------
     25x        = 51           --->  x = 51/25

3. Plug in this x value into equation (a) or (b) and solve for y. 

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