Question

Is the ordered pair (2,3) a solution of the system of linear equations -2x+3y=5 and 3x+2y=12?

Answer 1

Yes

Explanation:

Substituting `(color(red)(2),color(blue)(3))` for `(color(red)(x),color(blue)(y))`

• in `-2color(red)(x)+3color(blue)(y)`
  `color(white)("XXX")`gives `-2(color(red)(2))+3(color(blue)(3)) =-4+9 = 5`
  `color(white)("XXX")`So the given coordinates are a solution to the first equation.
• in `3color(red)(x)+2color(y)=12`
  `color(white)("XXX")`gives `3(color(red)(2))+2(color(blue)(3))=6+6 =12`
  `color(white)("XXX")`So the given coordinates are a solution to the second equation.

Since the given coordinates are a solution to both equations,
they are a solution to the system of equations.