Solving Algebra Equations

As far as solving algebra equations is concerned, this math topic, 'systems of equations' is one of the hardest to understand.

There are basically 2 methods used to solve systems of equations. Elimination and substitution method.

Now, depending on how awful and awkward your equation looks will depend on the method YOU decide to use. I will show you both methods here, however its up to you which method you learn.

I would recommend learning both as you never know your exam might just say, 'Solve this system of equation using the method of elimination' or 'solve this problem using the substitution method'. The gamble is yours.

Alternatively, to solve this dilemma just find out what your syllabus requires you to learn.

For a more advanced approach to solving simultaneous equations using Matlab check this fabulous resource.

Method 1

Solving Algebra Equations using the Elimination Method

Example 1

3x+y=3

x+y=1

We need to eliminate either the x or y from the equation. If we add the 2 equations we get

4x+2y=4. This has not eliminated either x or y. So lets subtract the equations instead, to give us

2x+0=2

2x=2, Now dividing both sides of the equation by 2 to get

2x/2=2/2, Cancel down the fractions to give

x=1, This is one solution.

Now substituting x=1 into one of the above equations to find y. Any will do, substituting into either will still give us the same answer. The trick is to substitute it into the easy equation, which appears to be the second one. ;)

x+y=1

1+y=1, Subtracting both sides of the equation by 1 to get

1-1+y=1-1, Therefore

y=0, This is the other solution

Write the solution down as such (1,0)

Example 2 (slightly harder)

-2x+3y=4 Equation A

4x+y=-1 Equation B

If you try to add or subtract either of the above equations it does not eliminate x's or y's. Therefore we have to manipulate the equations to get it to do what we want.

Lets start by multiply through equation B by 3 to get

12x+3y=-3

Next subtract equation A by this one to eliminate the y's,

The maths for this would look like this, -2x-12x+3y-3y=4--1

to give, -14x=5

Dividing through this equation by -14 to give

x=-5/14, This is one solution.

Next substitute x=-5/14 into equation A or B. The easiest looking equation is the best one to go for.

Lets go for equation B

4(-5/14)+y=-1

-20/14+y=-1

y=-1+1 3/7

y=3/7 This is the other solution

Writing it as an ordered pair (basically to make it look more mathematical and formal) (-5/14, 3/7)

Example 3

3x+2y=8

2x+5y=-2

Solution can be viewed here

Method 2

Solving Algebra Equations using the Elimination Method

(Come back later as this bit is Under Construction)

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