Question

Solve by subtitution 2x-3y=12 ; x=5y-12

Answer 1

x = 96/7

y = 36/7

Explanation:

Given equations:

2x-3y=12 ...(1)

x=5y-12 ...(2)

We have to solve this equation by substitution.

As given, from eqn (2), the value of x. This value of "x" can be substituted to the equation (1).

The equation (1) stands at:

• 2(x) - 3y = 12

Putting the value of x,

• 2(5y-12) - 3y = 12

Simplifying,

• 10y-24 -3y = 12( Distribution method on LHS)
• 7 y = 12 + 24 (Transpose 24 to the RHS )
• 7y = 36
• y = 36/7

Putting the value of y in eqn(2),

• x = 5y-12
• x = 5*36/7 -12 (Take LCM)
• x = (180-84)/7
• x = 96/7

Answer 2

2x-3y=12

x-5y= -12

per substitution : x =5y-12

we remplace x in 2x-3y=12

2(5y-12)-3y=12

10y-24-3y=12

7y =12+24

y=36/7

we calculate x :

x=5y-12

x=5*36/7 -12 = 96/7