Solving Simultaneous Non-Linear Equations Graphically
Author: Selina

Use the slider to change the values of  m1, c1, a, b and c to form a linear equation and a quadratic equation.

Solve these 2 equations by Substitution Method.

Observe the coordinates of the intersection points.

Is it true that the solutions of the 2 equations are always the x and y coordinates of the intersection points?

\textbf{Grafické riešenie sústavy nelineárnych rovníc}

k = 2 (slider from -10 to 10, step 1)
q = -1 (slider from -10 to 5, step 1)
a_1: y = (k * x) + q
text1: " \text{Lineárna funkcia:} \;  " + (LaTeX[a_1]) + ""
a = 1 (slider from -10 to 10, step 1)
b = 2 (slider from -10 to 10, step 1)
c = -5 (slider from -10 to 10, step 1)
d: y = (a * x^(2)) + (b * x) + c
text2: " \text{Kvadratická funkcia}: \;  " + (LaTeX[d]) + ""
A, B = Intersect(d, a_1)
e: x(A)
f: y(A)
g: x(B)
h: y(B)
text7: "M_1=" + (LaTeX[A]) + " "
text3: " \text{Riešenie 1.  bod } M_1= (" + (LaTeX[e]) + "," + (LaTeX[f]) + ")"
text6: "M_2 = " + (LaTeX[B]) + ""
text4: " \text{Riešenie 2.  bod } M_2 = (" + (LaTeX[g]) + "," + (LaTeX[h]) + ")"