SOLUTION: Find the points of intersection of the ellipse 16x^2 + 25y^2 = 400 and the line 5y + 4x = 20

Click here to see ALL problems on Graphs

Question 133357: Find the points of intersection of the ellipse 16x^2 + 25y^2 = 400 and the line 5y + 4x = 20

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
In order to solve this system

We need to isolate one variable and substitute that expression to eliminate one variable.

Start with the second equation

Subtract 4x from both sides

Divide both sides by 5 to isolate y

---------------

Go back to the first equation

Plug in . Notice how we eliminated the "y" terms and now have one equation with one unknown.

Distribute the outer exponent

Evaluate to get 25

Cancel like terms

Cancel like terms

Foil

Subtract 400 from both sides

Combine like terms

Factor out

Now set each factor equal to zero:

or

Now solve for x for each factor:

or

So our solutions are

or

So let's find y when

Start with the second equation

Plug in

Multiply and simplify

Divide both sides by 5 to isolate x

So when ,

So one intersection point is (0,4)

------------------------------------

So let's find y when

Start with the second equation

Plug in

Multiply and simplify

Subtract 20 from both sides

Divide both sides by 5 to isolate x

So when ,

So one intersection point is (5,0)

-----------------------------------------------------------

Answer:

So our solutions are (0,4) and (5,0)

Notice if we graph, we can visually verify our answer