Question

How do you solve the system of equations algebraically `3x-5y+z=9, x-3y-2z=-8, 5x-6y+3z=15`?

Answer 1

`(x,y,z)to(-6,-4,7)`

Explanation:

`"using the process of elimination"`

`color(blue)" eliminating z"`

`3x-5y+z=9to(1)`

`x-3y-2z=-8to(2)`

`5x-6y+3z=15to(3)`

`(2)+2xx(1)larr" row operation"`

`7x-13y=10to(4)`

`(3)-3xx(1)larr" row operation"`

`-4x+9y=-12to(5)`

`color(blue)" eliminating x"`

`4xx(4)+7xx(5)larr" row operation"`

`11y=-44tocolor(red)(y=-4)`

`"substituting in " (4)`

`7x+52=10tocolor(red)(x=-6)`

`"substituting in " (1)`

`-18+20+z=9tocolor(red)(z=7)`

`color(blue)"As a check"" in " (2)`

`-6+12-14=-8rarr" True"`

`rArr(-6,-4,7)" is the solution"`