Question

6x+y^2=10 and 3x-y=5 find all solutions and determine whether or not the system is linear or nonlinear?

Answer 1

`(1,-2)` and `(5/3,0)`
The system will be nonlinear because it includes a quadratic equation.

Explanation:

This is a system of equations, so solving one term one in terms of the other will allow you to find the solution

`-y=-3x+5`
`y=3x-5`

Then plug in the value of `y` into the first equation

`6x+(3x-5)^2=10`

Solve for `x`

`6x+9x^2-30x+25=10`
`9x^2-24x+15=0`
`3(x^2-8x+5)=0`
`3(x-1)(x-5/3)=0`

`x=1, 5/3`

Now that we know the x coordinates of the solutions, we can plug them into one of the equations to solve for the y coordinates

`3(1)-y=5`
`y=-2`

`3(5/3)-y=5`
`y=0`