Chapter 9.7, Problem 37PFA

To determine

To select equations which somplete system of equations.

Answer to Problem 37PFA

  $y=-x+3$

Explanation of Solution

Given information:

Quadratic equation

  $y=x^2+1$

Linear equations

  $1)y=1$

  $2)y=3$

  $3)y=x+2$

  $4)y=-x-2$

  $5)y=-x+3$

Formula used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

  $y=x^2+1$ with $y=-x+3$ has two solutions

  $y=x^2+1\mathrm{.......}(1)$

  $y=-x+3\mathrm{........}(2)$

Substituting $y=-x+3$ in equation (1)

  $-x+3=x^2+1$

On solving,

  $x^2+x-2=0$

  $a=1$

  $b=1$

  $c=-2$

Using formula

  $x=\frac{-1\pm \sqrt{1^2-4(1)(-2)}}{2(1)}$

On solving,

  $x=\frac{-1\pm 3}{2}$

On solving,

  $x=\frac{-1-3}{2}$ and $x=\frac{-1+3}{2}$

On solving,

  $x=-2,1$

If,

  $x=-2$

Then $y=5$

If,

  $x=1$

Then

  $y=2$