Mathematics 10 — Exercise 2.2 · Q3 (ii)

Full question

Draw the graphs of the following two equations on the same coordinate plane. Find their point(s) of intersection and hence solve the simultaneous equations.

Step-by-step solution

1. Write both equations as y = f(x) and y = g(x).

   $$(y=2-x,y=2\times x^2+x-10)$$

2. Compute and plot points for both curves. Their intersection is where they share x AND y.

3. Check the graph reading by setting the two expressions for y equal.

   $$2-x=2\times x^2+x-10$$

4. Move all terms to one side and solve for x.

   $$-2\times \left(x-2\right)\times \left(x+3\right)=0$$

5. Substitute each x into either equation for y.

   $$((-3,5),(2,0))$$

Answer

The final answer is shown below.