Question

How do solve the following linear system?: `5x + y = 9 , 3x+ 2y - 3 = 0`?

Answer 1

`(x,y)to(15/7,-12/7)`

Explanation:

`5x+y=9to(1)`

`3x+2y-3=0to(2)`

`"rearrange "(1)" expressing y in terms of x"`

`"subtract "5x" from both sides"`

`y=9-5xto(3)`

`"substitute "y=9-5x" into equation "(2)`

`3x+2(9-5x)-3=0`

`3x+18-10x-3=0`

`-7x+15=0`

`"subtract 15 from both sides"`

`-7x=-15`

`"divide both sides by "-7`

`(cancel(-7) x)/cancel(-7)=(-15)/(-7)rArrx=15/7`

`"substitute "x=15/7" in equation "(3)`

`y=9-75/7=63/7-75/7=-12/7`

`"point of intersection "=(15/7,-12/7)`