Topics
19. Simultaneous Equations
topic badge
iGCSE (2021 Edition)

19.04 Non-linear Simultaneous Equations (Extended)

Lesson
Worksheet
Worksheet
Non-linear simultaneous equations
1

Solve the following systems of equations:

a
\begin{aligned} y &= x^{2} \\ y &= 4 x \end{aligned}
b
\begin{aligned} y &= 2x \\ y &= x^{2} +6x \end{aligned}
c
\begin{aligned} x^{2} + y &= 2 \\ y &= x - 4 \end{aligned}
d
\begin{aligned} y &= x^{2} - 16 \\ y &= x-16 \end{aligned}
e
\begin{aligned} x^2 + y &= 10 \\ 2x-y &= 5 \end{aligned}
f
\begin{aligned} x^{2} + y &= 5 \\ - 2 x + y &= 5 \end{aligned}
g
\begin{aligned} y &= x^{2} + 2 \\ y &= 4- x \end{aligned}
h
\begin{aligned} y &= \left(x - 2\right)^{2} \\ y &= 8 - x \end{aligned}
i
\begin{aligned} y &= x^{2} - 9 x - 6 \\ y &= x + 5 \end{aligned}
j
\begin{aligned} y &= 2 x^{2} -8 x +10 \\ y &= 4 x -8 \end{aligned}
k
\begin{aligned} y &= - 2 x^{2} - 3 x + 7 \\ y &= 4 x -8 \end{aligned}
l
\begin{aligned} y &= 2 x^{2} + 4 x + 2 \\ y &= 2 x +6 \end{aligned}
2

Approximate the solutions of the following systems of equations by graphing the functions on a number plane and approximating their points of intersection. Round your values to one decimal place.

a
\begin{aligned} y &= x^{2} -4 \\ y &= x-1 \end{aligned}
b
\begin{aligned} y &= x+4 \\ y &= 8-x^2 \end{aligned}
Applications
3

The sum of two numbers is 60. The larger number equals the smaller number squared plus 4.

a

Set up two equations by letting x and y be the two numbers, where y is the larger of the two numbers.

b

Find all the solutions for x and y. Write your answers as ordered pairs.

4

In business, supply and demand functions are ways of expressing the supply or demand of a commodity as a function of its unit price. Market equilibrium is the term that describes when the supply is equal to the demand. Consider the supply and demand functions for a new book bag below, where y is in dollars and x is in thousands of units supplied:

  • Supply function: y = 2 x^{2}

  • Demand function: y = 4 x + 6

a

Solve the equations for x.

b

Which of these values of x must the equilibrium point be at? Explain your answer.

c

Find the value of y for this value of x.

d

Complete the following statement:

The equilibrium quantity occurs when ⬚ thousand units are being produced, which has a corresponding price of ⬚ dollars per unit.

Sign up to access Worksheet
Get full access to our content with a Mathspace account
Book a Demo
Sign up for free

Outcomes

0580E2.5C

Derive and solve simultaneous equations, involving one linear and one quadratic.

What is Mathspace

About Mathspace