Question

How do you solve each system of equations and then check the answer algebraically? 11) -6x+3y=33 -4x+y=16 12)2y=5x-1 x+y=-1

Answer 1

`"see explanation"`

Explanation:

`(11)`

`-6x+3y=33to(1)`

`-4x+y=16to(2)`

`"from "(2)color(white)(x)y=16+4xto(3)`

`color(blue)"Substitute "y=16+4x" in equation "(1)`

`-6x+3(16+4x)=33`

`rArr-6x+48+12x=33`

`rArr6x+48=33`

`"subtract 48 from both sides"`

`6xcancel(+48)cancel(-48)=33-48`

`rArr6x=-15`

`"divide both sides by 6"`

`(cancel(6) x)/cancel(6)=(-15)/6`

`rArrx=-15/6=-5/2`

`"substitute this value in equation "(3)`

`rArry=16+(4xx-5/2)=16-10=6`

`rArr(x,y)to(-5/2,6)`

`color(blue)"As a check"`

`"substitute the solution into either of the 2 equations"`

`(2)to(-4xx-5/2)+6=10+6=16larr" True"`

`"this confirms that "(-5/2,6)" is the solution"`

`(12)`

`"the solution is "(x,y)to(-1/7,-6/7)`

`"this is done in exactly the same way as 11"`

`"you may wish to try it for yourself"`