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Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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The solutions to a system of equations are the points of intersection of the lines. For a system with two quadratic equations, there are 4 cases to consider: 2 solutions, 1 solution, no solutions, and infinite solutions.

Basic concepts: System of linear-quadratic equations, 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,

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

• For a system consisting of two quadratic equations:

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

quadratic equation: $y = d{x^2} + ex + f$

There are 4 cases to consider:case 1: 2 solutions case 2: 1 solution case 3: no solutions case 4: infinite solutions

- 2.
**Case 1: System with 2 Solutions**

Solve the system, then verify the solutions graphically:

$y = {x^2} - 6x + 5$

$y = - 2{x^2} + 9x - 7$

- 3.
**Case 2: System with 1 Solution**

Solve the system, then verify the solutions graphically:

$y = 2{x^2} + 6x + 7$

$y = - {x^2} + 4$

- 4.
**Case 3: System with No Solutions**

Solve the system, then verify the solutions graphically:

$y = - {x^2} + 6x - 10$

$y = 2{x^2} + 6x + 5$

- 5.
**Case 4: System with Infinite Solutions**

Solve the system, then verify the solutions graphically:

${x^2} - 4x - y + 3 = 0$

$5y - 5{x^2} + 20x - 15 = 0$

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 (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