# Solve systems of linear equations Ax = B for x

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Johan Johan on 29 Aug 2019
Edited: Stephen Cobeldick on 29 Aug 2019
x = A\B solves the system of linear equations A*x = B. The matrices A and B must have the same number of rows.
But ,what is the operation between the rows?
There is any one can solve this example–manually ?
A =
1 3
4 2
b= [6 ;7];
>> A\b
ans =
0.9000
1.7000
How to find 0.9 and 1.7 exactly?

Stephen Cobeldick on 29 Aug 2019
Edited: Stephen Cobeldick on 29 Aug 2019
"But ,what is the operation between the rows?"
Both mldivide and mrdivide can use many different algorithms for solving systems of linear equations, as documented in the mldivide documentation. There is no single "operation" that describes all of those algorithms.
"There is any one can solve this example–manually ?"
This is easy using standard definitions for solving linear equations, e.g. elimination of variables:
System definition:
First solve the first equation for x:
Second, substitute x back into the second equation:
Third, solve that for y:
And finally try them with your example values:
>> A = [1,3;4,2]
A =
1 3
4 2
>> b = [6;7]
b =
6
7
>> A\b
ans =
0.9
1.7
>> y = (A(1,1)*b(2)-A(2,1)*b(1)) ./ (A(1,1)*A(2,2)-A(2,1)*A(1,2))
y =
1.7
>> x = (b(1)-A(1,2)*y) ./ A(1,1)
x =
0.9

KALYAN ACHARJYA on 29 Aug 2019
Edited: KALYAN ACHARJYA on 29 Aug 2019
ans =
0.9000
1.7000
How to find 0.9 and 1.7 exactly??
format shortg;
A =[1 3
4 2];
b= [6 ;7];
A\b
Result:
ans =
0.9
1.7