The point (3, 2) is the solution to given system of equations
Solution:
Given that system of equations are:
------ eqn 1
------- eqn 2
From eqn 2,
y = 2x - 4
Substitute y = 2x - 4 in eqn 1
![x^2 + (2x - 4)^2 = 13\\\\x^2 + 4x^2 + 16 - 16x = 13\\\\5x^2 -16x + 3 = 0](/tpl/images/0427/2495/b02d1.png)
Let us solve the above equation by quadratic formula,
![\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}](/tpl/images/0427/2495/c39d1.png)
Using the Quadratic Formula for
where a = 5, b = -16, and c = 3
![\begin{aligned}&x=\frac{-(-16) \pm \sqrt{(-16)^{2}-4(5)(3)}}{2 \times 5}\\\\&x=\frac{16 \pm \sqrt{256-60}}{10}\\\\&x=\frac{16 \pm \sqrt{196}}{10}\end{aligned}](/tpl/images/0427/2495/fa433.png)
The discriminant
so, there are two real roots.
![\begin{aligned}&x=\frac{16 \pm \sqrt{196}}{10}=\frac{16 \pm 14}{10}\\\\&x=\frac{16+14}{10} \text { or } \frac{16-14}{10}\\\\&x=\frac{30}{10} \text { or } x=\frac{2}{10}\\\\&x=3 \text { or } x=0.2\end{aligned}](/tpl/images/0427/2495/bc26c.png)
Substitute for x = 0.2 and x = 3 in 2x - y = 4
when x = 3
2(3) - y = 4
6 - y = 4
y = 2
when x = 0.2
2(0.2) - y = 4
0.4 - y = 4
y = 0.4 - 4
y = -3.6
Thus Option D is correct The point is (3, 2)