System of linear equations

System of linear equations means a set or collection of linear equations, that we deal with all together at once. As we know dealing with linear equations is more simpler than dealing with non linear equations.

A solution for the system of equations is a point that lies on each lines of the given equations

Example 1:
Determine whether either of the points (11, 17) and (-4, 3) is a solution to the given system of linear equations:

y= 2x-5

y= x+6

Solution: To check the possible solutions, let us plug in the x and y value in the given equations.

Point (11, 17)

for the equation y=2x-5

17 = 2*(11)-5

17 = 22-5

17 = 17

for the equation y=x+6

17 = 11+6

17 = 17

So (11, 17) is a solution


for the equation y= 2x-5



3=-13, which is not equal.

for the equation y=x+6


3=2, which is not equal.

so (-4,3) is not a solution

Example 2:
If the point (4,-2) lies on the line 5x + 2y +k = 0.Find the value of k.

Solution: Here the given point (4,-2) lies on the given line.To solve this problem we have to apply the given points in the equation as the value of x and y.

Point (4,-2)

Here x = 4 and y = -2

The given equation is 5x 2y + k = 0
applying the values of x and y we are getting 5(4) + 2 (-2) + k = 0

20 - 4 + k = 0
16 + k = 0
k = -16
So the value of k is -16

By using the concept system of linear equations,we can solve many problems which we have in our daily life.

Example: When I went shopping, I paid $21 for 5 pens and 3 pencils, i paid $24 for 4 pens and 6 pencils.What is the cost of each pen and pencil?

In our daily life, We have many problems like the above example. To solve this kind of real problems, we have to use system with linear equations.When this kind of question is had by the students in exam or in their homework, they may find it difficult to do and find the solution.if they apply concept of linear equations here, easily they can solve the problems and get solutions.

Related topics of system of linear equations

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

             Math dictionary