*In our example equation set, for instance, we may add ) into one of the original equations.In this example, the technique of adding the equations together worked well to produce an equation with a single unknown variable.*

The step-by-step example shows how to group like terms and then add or subtract to remove one of the unknowns, to leave one unknown to be solved.

It involves what it says − substitution − using one of the equations to get an expression of the form ‘y = …’ or ‘x = …’ and substituting this into the other equation.

Let’s take our two-variable system used to demonstrate the substitution method: One of the most-used rules of algebra is that you may perform any arithmetic operation you wish to an equation so long as you do it equally to both sides.

With reference to addition, this means we may add any quantity we wish to both sides of an equation—so long as its the same quantity—without altering the truth of the equation.

Take, for instance, our two-variable example problem: In the substitution method, we manipulate one of the equations such that one variable is defined in terms of the other: Then, we take this new definition of one variable and substitute it for the same variable in the other equation.

In this case, we take the definition of : Applying the substitution method to systems of three or more variables involves a similar pattern, only with more work involved.This gives an equation with just one unknown, which can be solved in the usual way.This value is then substituted in one or other of the original equations, giving an equation with one unknown.It is especially impractical for systems of three or more variables.In a three-variable system, for example, the solution would be found by the point intersection of three planes in a three-dimensional coordinate space—not an easy scenario to visualize.This is then substituted into one of the otiginal equations.The 2 lines represent the equations '4x - 6y = -4' and '2x 2y = 6'. Because the graphs of 4x - 6y = 12 and 2x 2y = 6 are straight lines, they are called linear equations.What about an example where things aren’t so simple?Consider the following equation set: We could add these two equations together—this being a completely valid algebraic operation—but it would not profit us in the goal of obtaining values for : The resulting equation still contains two unknown variables, just like the original equations do, and so we’re no further along in obtaining a solution.An option we have, then, is to add the corresponding sides of the equations together to form a new equation.Since each equation is an expression of equality (the same quantity on either side of the sign), adding the left-hand side of one equation to the left-hand side of the other equation is valid so long as we add the two equations’ right-hand sides together as well.

## Comments Solving Problems Using Simultaneous Equations

## Simultaneous Equations - Mathematics GCSE Revision

Simultaneous equations and linear equations, after studying this section, you will be able to. Solving simultaneous linear equations using straight line graphs. The 2 lines represent the equations '4x - 6y = -4' and '2x + 2y = 6'. There is only one point the two equations cross.…

## Solving systems of equations by elimination video Khan.

Let's explore a few more methods for solving systems of equations. Let's say I have the equation, 3x plus 4y is equal to 2.5. And I have another equation, 5x minus 4y is equal to 25.5. And we want to find an x and y value that satisfies both of these equations.…

## Solving Simultaneous Equations and Matrices -

Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering this relatively simple problem is to illustrate how matrix notation and algebra can be developed and used to consider problems such as…

## Solving Simultaneous Equations using Matrices solutions.

How to use matrices to solve simultaneous equations or systems of equations, How to use the inverse of a matrix to solve a system of equations, with examples and step by step solutions, how to solve a system of equations by using a matrix equation, 3x3 matrix equation example, 2x2 matrix equation example, solving 3 simultaneous equations using matrices…

## Solving word problems using equations by Maths2Measure.

A worksheet with worked solutions. Students need to use a pronumeral to represent the unknown number They then need to write an equation and solve it to find the value of the unknown number. Australian Curriculum NSW MA4-8NA generalises numb.…

## How to Solve Simultaneous Equations Graphically 8 Steps

There are a few ways to solve simultaneous equations; one of them is to plot the lines of the 2 equations, thus solving the equation. This article will teach you how to solve simultaneous equations graphically! Steps. 1. Write your 2 equations clearly. Write your 2 equations in an organised, clear way. This will make it easier later.…

## Solving Systems of Linear Equations Using Matrices

Solving Systems of Linear Equations Using Matrices Hi there! This page is only going to make sense when you know a little about Systems of Linear Equations and Matrices, so please go and learn about those if you don't know them already! The Example. One of the last examples on Systems of Linear Equations was this one…

## Simultaneous linear equations - A complete course in algebra

In this case, the solution is not obvious. Here is a general strategy for solving simultaneous equations When one pair of coefficients are negatives of one another, add the equations vertically, and that unknown will cancel. We will then have one equation in one unknown, which we can solve. Upon adding those equations, the y's cancel…