Question

Using elimination method solve the equation
7(a+b) = 7(y-x)
5(3x-y) = x+3

Answer 1

see the explanation

Explanation:

we have

`7(a+b)=7(y-x)`

simplify

`(a+b)=(y-x)` -----> equation A

`5(3x+y)=x+3`

`15x+5y=x+3\\14x+5y=3`

Rewrite

`3=14x+5y` -----> equation B

Solve by elimination method

Multiply equation A by 14 both sides

`14(a+b)=14y-14x` -----> equation C

Adds equation B and equation C

`3=14x+5y\\14(a+b)=14y-14x\\-----------\\3+14(a+b)=5y+14y\\3+14(a+b)=19y`

`y=(3+14(a+b))/(19)`

Find the value of x

substitute the value of y in the equation B

`3=14x+5((3+14(a+b))/(19))`

`14x=3-5((3+14(a+b))/(19))`

`x=(3)/(14)-(5)/(14)((3+14(a+b))/(19))`