Question

How do you solve `3x + 5y = 25` and `- 3x - 4y = - 23`?

Answer 1

`x=7.5" , "y=1/2`

Explanation:

`3x+5y=25" (1)"`
`-3x-4y=-23" (2)"`

`"let us add the equations above to eliminate value x"`

`3x+5y-3x-4y=25-23`

`cancel(3x)+5ycancel(-3x)-4y=25-23`

`5y-4y=25-23`

`4y=2`

`y=2/4`

`color(red)(y=1/2)`

`3x+5y=25" (1)"`

`3x+5*color(red)(1/2)=25`

`3x=25-5/2`

`3x=color(green)(2/2)*25-5/2`

`3x=50/2-5/2`

`3x=(50-5)/2`

`3x=45/2`

`"if "color(blue)(a/b=c/ d)" then "color(blue)(a*d=b*c)`

`(3x)/1=45/2`

`3x*2=1*45`

`6x=45`

`(6x)/(6)=(45)/6`

`(cancel(6)x)/(cancel(6))=(45)/6`

`x=45/6`

`x=7.5`