Quadratic Simultaneous Equations – GCSE Maths

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Introduction

  • Two or more equations that share variables and have set of values for variables that satisfy both the equations are called Simultaneous Equations.
  • If the maximum power raised to the variable in Simultaneous equations is one then these are called Linear Simultaneous Equations.
  • Similarly If the power raised to the variables is two they are called Quadratic Simultaneous Equations.

Step by Step Solving Quadratic Simultaneous Equations

Example: Problem for step by step solving of a quadratic simultaneous equations with variable x and yStep#1: Substitute the value of one variable from linear equation(to eliminate one variable) –

Putting y = 2x -1 in 2nd equation –solution of x and y quadratic simultaneous equations with variable x and yStep#2: Substitute the values obtained back into the original equation and find possible values of another variable-

For x = -3 from 1st Equation-solution of x and y quadratic simultaneous equationFor x = 2 from 1st Equation

solution of x and y equationStep#3: Final Answer –Step by step solved example final answer quadratic simultaneous equations for maths gcse

certified Physics and Maths tutorSolved Example:

Problem: Equation for solved examples of quadratic simultaneous equations with variables x and ySolution:

Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-

From 1st Equation-Equation for solved examples with variables x and yPut in 2nd Equation-Solution of Equation for solved examples of quadratic simultaneous equations with variables x and yStep#2: Substitute the values obtained back into the original equation and find possible values of another variable-

Put x = -2 in 1st Equation –Solution of Equation for solved examples of quadratic simultaneous equations with variables x and yPut x = 7 in 1st Equation –Solution of Equation for solved examples with variables x and y

Step#3:Final Answer-Final answer for solved example 1

certified Physics and Maths tutorSolved Example:

Problem: Equation for solved examples of equations with variables x and ySolution:

Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-

From 1st Equation,

Solution of Equation for solved examples with variables x and y

Put in 2nd Equation,

Solution of Equation for solved examples of quadratic simultaneous equations with variables x and y

Divide by 2 on both sides and doing factorisation-Solution of Equation for solved examples of quadratic simultaneous equations with variables x and yStep#2: Substitute the values obtained back into the original equation and find possible values of another variable-

Put y = 4 in 1st Equation –equation to find 1st value of x for solved example of equation with variables x and yPut y = 8 in 1st Equation –equation to find 2nd value of x for solved example of quadratic simultaneous equations with variables x and yStep#3: Final Answer-Final answer for solved example 2

certified Physics and Maths tutorSolved Example:

Problem: Equation for solved examples of equations with variables x and y for gcse mathsSolution:

Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-

From 1st Equation-

Solution of Equation for solved examples of quadratic simultaneous equations with variables x and yPut in 2nd Equation-

Calculations to find value of x for step by step solved example with variables x and y for gcse math

Step#2: Substitute the values obtained back into the original equation and find possible values of another variable-

Put x = -3 in 1st Equation –Calculations to find value of y for step by step solved example of quadratic simultaneous equations with variables x and y for gcse mathPut x = 12 in 1st Equation –Calculations to find value of y for step by step solved example with variables x and y for gcse mathStep#3: Final Answer-final answer of solved example no 3

certified Physics and Maths tutorSolved Example:

Problem: Solution of Equation for solved examples of quadratic simultaneous equations with variables x and y for gcse mathsSolution:

Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-

From 1st Equation,

Solution of Equation for solved examples of quadratic simultaneous equations with variables x and yPut in 2nd Equation,

Solution after substitution of value of y in 1st equation with variables x and y for gcse maths revision and practiceDivide by 2 on both sides-Values of x for solved example number 4 for equation with variable x and yStep#2: Substitute the values obtained back into the original equation and find possible values of another variable-

Put x = 1 in 2nd Equation –value of y for solved examplePut x = -2 in 2nd Equation –value of y for solved exampleStep#3: Final Answer-Final answer with 2 values of x and y

certified Physics and Maths tutorSolved Example:

Problem: Equation for solved examples of quadratic simultaneous equations with variables x and y for gcse mathsSolution:

Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-

From 1st Equation,

Solution of Equation for solved examples of quadratic simultaneous equations with variables x and yPut in 2nd Equation-Solution after substitution of value of y in 1st equation with variables x and y for gcse maths revision and practiceStep#2: Substitute the values obtained back into the original equation and find possible values of another variable-

Put x = 1 in 2nd Equation –1st value of y for solved examplePut x = -4 in 2nd Equation –2nd value of y for solved exampleStep#3: Final Answer-Final answer solved example number 5

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