solve this linear equation in two variable
Answers
(3x-6)/3 = (y+4)/2 = (5x+5y)/17
step 1 :-
(3x-6)/3 = (y+4)/2
cross multiply it, you will get this :
6x - 3y = 24
divide this equation by 3, then simplified equation formed
2x - y = 8 ------- equation 1
step 2 :-
(3x-6)/3 = (5x+5y)/17
cross multiply it, you will get this :
36x - 15y = 102
divide this equation by 3, then simplified equation formed
12x - 5y = 34 ------- equation 2
Now,
2x - y = 8 -------- *5 (multiply by 5 to make coefficient of y equal to eq 2)
10x - 5y = 40 ------- equation 3
12x - 5y = 34 ------- *1
12x- 5y = 34 -------- equation 4
Now solve,
10x - 5y = 40
12x- 5y = 34
(-) (+) (-)
--------------------
-2x = 6
-2x = 6
x = -3
10x - 5y = 40
10(-3) - 5y = 40
-30 - 5y = 40
-5y = 40 + 30
-5y = 70
y = -14
Question:
Solve the following linear equation in two variables:
( 3x - 6 ) / 3 = ( y + 4 ) / 2 = 5 ( x + y ) / 17
Answer:
The solution of the given equation is ( x, y ) = ( - 3, - 14 ).
Step-by-step-explanation:
The given equation is
( 3x - 6 ) / 3 = ( y + 4 ) / 2 = 5 ( x + y ) / 17
We have to find the values of x and y.
Now,
( 3x - 6 ) / 3 = ( y + 4 ) / 2 = 5 ( x + y ) / 17
∴ ( 3x - 6 ) / 3 = ( y + 4 ) / 2
⇒ 3 ( x - 2 ) / 3 = ( y + 4 ) / 2
⇒ x - 2 = ( y + 4 ) / 2
⇒ 2 ( x - 2 ) = y + 4
⇒ y + 4 = 2x - 4
⇒ y = 2x - 4 - 4
⇒ y = 2x - 8 - - - ( 1 )
Now,
( y + 4 ) / 2 = 5 ( x + y ) / 17
⇒ ( 2x - 8 + 4 ) / 2 = 5 ( x + 2x - 8 ) / 17 - - - [ From ( 1 ) ]
⇒ ( 2x - 4 ) / 2 = 5 ( 3x - 8 ) / 17
⇒ 2 ( x - 2 ) / 2 = ( 15x - 40 ) / 17
⇒ x - 2 = ( 15x - 40 ) / 17
⇒ 17 ( x - 2 ) = 15x - 40
⇒ 17x - 34 = 15x - 40
⇒ 17x - 15x = - 40 + 34
⇒ 2x = - 6
⇒ x = - 6 ÷ 2
⇒ x = - 3
By substituting x = - 3 in equation ( 1 ), we get,
y = 2x - 8 - - - ( 1 )
⇒ y = 2 * ( - 3 ) - 8
⇒ y = - 6 - 8
⇒ y = - 14
∴ The solution of the given equation is ( x, y ) = ( - 3, - 14 ).