Question

How do you solve the system of equations `x^2+6y^2=40` and `y^2-3x^2=-44` by the elimination method?

Answer 1

`(-4,+-2),(4,+-2)`

Explanation:

`x^2+6y^2=40to(1)`

`y^2-3x^2=-44to(2)`

`"rearranging equation "(1)" gives"`

`x^2=40-6y^2to(3)`

`color(blue)"substitute "x^2=40-6y^2" into "(2)`

`y^2-3(40-6y^2)=-44`

`y^2-120+18y^2=-44`

`19y^2-120=-44`

`"add 120 to both sides"`

`19y^2=-44+120=76`

`"divide both sides by 19"`

`y^2=76/19=4`

`color(blue)"take the square root of both sides"`

`y=+-sqrt4=+-2`

`"substitute "y=+-2" into equation "(3)`

`x^2=40-24=16`

`x=+-4`

`"solutions are "(-4,+-2),(4,+-2)`
graph{(x^2+y^2-40)(y^2-3x^2+44)=0 [-20, 20, -10, 10]}