SOLUTION: Hi need help please in solving all values of x and y and can you please show me each step this is another one 1. x^2 - 3y^2 = 13 x

SOLUTION: Hi need help please in solving all values of x and y and can you please show me each step this is another one 1. x^2 - 3y^2 = 13 x - 2y = 1

Question 188362: Hi need help please in solving all values of x and y and can you please show me each step this is another one
1. x^2 - 3y^2 = 13
x - 2y = 1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Add 2y to both sides to isolate "x".

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

Move onto the first equation

Plug in

FOIL

Subtract 13 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for y

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the answers for "y" are or

Now simply plug each solution of "y" into to find "x"

Plug in

So one set of solutions is and giving us the ordered pair (or point of intersection) (5,2)

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

Plug in

This means that another set of solutions is and giving us the ordered pair (or point of intersection) (-11,-6)

Here's a graph to visually confirm the answer:

Graph of (red) and (blue) with the intersection points (-11,-6) and (5,2) (black points)
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