Question

How do you solve `3a+b=4` and `a-2b=6` using substitution?

Answer 1

`(a,b)to(2,-2)`

Explanation:

`3a+b=4to(1)`

`a-2b=6to(2)`

`"from equation "(2)" we obtain "a=6+2bto(3)`

`color(blue)"substitute "a=6+2b" into equation "(1)`

`rArr3(6+2b)+b=4`

`rArr18+6b+b=4`

`rArr18+7b=4`

`"subtract 18 from both sides"`

`cancel(18)cancel(-18)+7b=4-18`

`rArr7b=-14`

`"divide both sides by 7"`

`(cancel(7) b)/cancel(7)=(-14)/7`

`rArrb=-2`

`color(blue)"substitute "b=-2" in equation "(1)`

`3a-2=4`

`rArr3a=4+2=6`

`rArra=6/3=2`

`"the solution is "a=2,b=-2`