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How to solve the system of linear equations in a easy way?

How to solve the system of linear equations in a easy way?

Grade:12

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago

Dear Suresh

Solving systems of equations graphically is one of the easiest ways to solve systems of simple equations

Another way to solve systems of equations is by substitution.  In this method, you solve on equation for one variable, then you substitute that solution in the other equation, and solve.  Example:


1. Problem: Solve the following system:
x + y = 11
3x - y = 5

Solution:
Solve the first equation for y
(you could solve for x - it
doesn't matter).

y = 11 - x

Now, substitute 11 - x for y
in the second equation. This gives
the equation one variable, which
earlier algebra work has taught
you how to do.

3x - (11 - x) = 5
3x - 11 + x = 5
4x = 16
x = 4

Now, substitute 4 for x in
either equation and solve for y.
(We use the first equation below.)

4 + y = 11
y = 7

Solve the following system:
x + y + z = 4
x - 2y - z = 1
2x - y - 2z = -1

Solution:
Start out by multiplying the
first equation by -1 and add
it to the second equation to
eliminate x from the second
equation.

-x - y - z = -4
x - 2y - z = 1
----------------
-3y - 2z = -3

Now eliminate x from the third
equation by multiplying the first
equation by -2 and add it to
the third equation.

-2x - 2y - 2z = -8
2x - y - 2z = -1
------------------
-3y - 4z = -9

Next, eliminate y from the third
equation by multiplying the second
equation by -1 and adding it to
the third equation.

3y + 2z = 3
-3y - 4z = -9
--------------
-2z = -6

Solve the third equation for z.

-2z = -6
z = 3

Substitute 3 for z in the
second equation and solve for y.

-3y - 2z = -3
-3y - 2(3) = -3
-3y - 6 = -3
-3y = 3
y = -1

Lastly, substitute -1 for y and
3 for z in the first equation
and solve for x.

x + (-1) + 3 = 4
x + 2 = 4
x = 2

All the best.

AKASH GOYAL

AskiitiansExpert-IITD

 

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