Question

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Note:This is not a question!This is my new series of Tutorials,in this one I am taking up the topic "LINEAR EQUATIONS PART 2, Inequalities included" because i see a major part of the questions asked in OS maths section is something like "SOLVE the above 2 linear equation" "use substitution method to solve " " how to do elImination method ", etc.

So here we go .Do not forget to provide your valuable feedback.Feel free to link this tutorial to students when they ask these types of questions again. Happy openstudying !

Answer 1

\[\huge \text{SYSTEM OF LINEAR EQUATIONS}\]

Answer 2

A system of linear equations means two or more linear equations. (In plain speak: 'two or more lines') If these two linear equations intersect, that point of intersection is called the solution to the system of linear equations.

Answer 3

\[\bf \rm \large \text{SOLUTION OF A SYSTEM OF LINEAR EQUATIONS}\]

Answer 4

The solution is where the equations 'meet' or intersect. The black point C on the fig below is the solution of the system.

Answer 5

So How many solutions can systems of linear equation have?

There can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below. Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case--a stem with exactly 2 lines.

Answer 6

Case I: 1 Solution
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This is the most common situation and it involves lines that intersect exactly 1 time.
The fig I showed above belongs to this case .

Answer 7

Case 2: No Solutions
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This only happens when the lines are parallel. As you can see, parallel lines are not going to ever meet.

Example of a stem that has no solution:

Line 1: \(\rm y = 5x +13\)
Line 2: \(\rm y = 5x + 12\)

Answer 8

Case 3: Infinite Solutions
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This is the rarest case and only occurs when you have the same line.

Consider, for instance, the two lines below \(\rm y = 2x+1\) and \(\rm 2y = 4x +2\). These two equations are really the same line .
Example of a system that has infinite solutions:
Line 1: y = 2x + 1
Line 2: 2y = 4x + 2

Answer 9

\[\large \bf \rm \text{SOLVING A SYSTEM OF LINEAR EQUATIONS}\]

Answer 10

There are several good ways to solve systems of linear equations, andthe best method to use in any given situation is the one that requires the least amount of work. However, that will depend on the particular equations that you’re trying to solve. The most popular methods are inspection, elimination, substitution, intersection, and graphing . I would like to provide a bonus method ,anyone who have gone through my previous tutorials can easily guess it .Yep I am speaking about vedic method !

Answer 11

\[\large \text{The Graph Method }\]

Answer 12

Example 1

What is the solution of the following system of equations?
\[\rm y=x+1 \\ y=2x\]

Answer 13

the graph is drawn above by my friend @whpalmer4 thanks :)

so the solution is \((1,2)\)