Question

How do you solve `3x+y=5` and `2x- y=20` using substitution?

Answer 1

`(x,y)to(5,-10)`

Explanation:

`3x+y=5to(1)`

`2x-y=20to(2)`

`"Rearrange equation "(1)" to express y in terms of x"`

`"subtract 3x from both sides"`

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

`rArry=5-3xto(3)`

`color(blue)"Substitute "y=5-3x" in equation "(2)`

`2x-(5-3x)=20`

`rArr2x-5+3x=20`

`rArr5x-5=20`

`"add 5 to both sides"`

`5xcancel(-5)cancel(+5)=20+5`

`rArr5x=25`

`"divide both sides by 5"`

`(cancel(5) x)/cancel(5)=25/5`

`rArrx=5`

`"substitute "x=5" into equation "(3)`

`rArry=5-(3xx5)=-10`

`rArr"solution is "(5,-10)`