Still Confused?

Try reviewing these fundamentals first

- Home
- GCSE Maths
- Simultaneous Equations

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

Nope, got it.

That's the last lesson

Start now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started Now- Intro Lesson2:34
- Lesson: 1a10:28
- Lesson: 1b3:19
- Lesson: 2a6:50
- Lesson: 2b6:53
- Lesson: 3a5:46
- Lesson: 3b3:20

The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.

Basic Concepts: Solving systems of linear equations by graphing, Solving systems of linear equations by elimination, Solving systems of linear equations by substitution, Solving quadratic equations by factoring, Solving quadratic equations using the quadratic formula

Related Concepts: Graphing linear inequalities in two variables, Graphing systems of linear inequalities, Graphing quadratic inequalities in two variables, Graphing systems of quadratic inequalities

- Introduction• The solutions to a system of equations are the points of intersection of the graphs.

• For a system consisting of a linear equation and a quadratic equation:

linear equation: $y = mx + b$

quadratic equation: $y = a{x^2} + bx + c$

There are 3 cases to consider:

case 1: 2 solutions case 2: 1 solution case 3: no solutions

- 1.
**Case 1: System with 2 Solutions**a)Solve the system:

$y = - x + 1$

$y = {x^2} + x - 2$b)Verify the solutions graphically - 2.
**Case 2: System with 1 Solution**a)Solve the system:

$2x - y = 8$

$y = {x^2} - 4x + 1$b)Verify the solutions graphically - 3.
**Case 3: System with No Solutions**a)Solve the system:

$10x + 5y + 15 = 0$

$y = {x^2} - 4x + 2$b)Verify the solutions graphically

17.

Simultaneous Equations

17.1

Determining number of solutions to linear equations

17.2

Solving simultaneous linear equations by graphing

17.3

Solving simultaneous linear equations by elimination

17.4

Solving simultaneous linear equations by substitution

17.5

Money related questions in linear equations

17.6

Unknown number related questions in linear equations

17.7

Distance and time related questions in linear equations

17.8

Rectangular shape related questions in linear equations

17.9

Simultaneous linear-quadratic equations

17.10

Simultaneous quadratic-quadratic equations

17.11

Solving 3 variable simultaneous equations by substitution

17.12

Solving 3 variable simultaneous equations by elimination

17.13

Solving 3 variable simultaneous equations with no solution, infinite solutions

17.14

Word problems relating 3 variable simultaneous equations

We have over 1720 practice questions in GCSE Maths for you to master.

Get Started Now17.1

Determining number of solutions to linear equations

17.3

Solving simultaneous linear equations by elimination

17.4

Solving simultaneous linear equations by substitution

17.5

Money related questions in linear equations

17.6

Unknown number related questions in linear equations

17.7

Distance and time related questions in linear equations

17.8

Rectangular shape related questions in linear equations

17.9

Simultaneous linear-quadratic equations

17.10

Simultaneous quadratic-quadratic equations