Solving Linear Equations

Question

While solving linear equations with two variables we can use simple method to calculate both the variables.

let us see an example of two equations and the method of calculation.

Answer 1

For Example linear equations:

x+3y=8 - equation 1

2x−9=y equation 2

We need to find the value of x and y

Let us put the value of y from equation 2 into equation 1

This gives us: x+3(2x-9)=8

Next step : x+6x-27=8

7x=35;

x=5

Now we have x=5 ; Let's find y

y=2x-9 as we have in equation 2

y=2*5-9=10-9=1

y=1

Final answer (5,1)

Answer 2

For the more advanced students

use matrix inverse, in this example matrix algebra is

[1 3}x=8

[2 -1}y=9

using matrix invese

x*determinant=[-1,-3}8

y*determinant=[-2 1]9

x*(-7)=-35

y*(-7)=-7