Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

\[
x + 3y = 9
\]

\[
3x - y = 7
\]

{ 3 x − y = 7 ( − 1 ) x + 3 y = 9 ( 3 ) ​ { − 3 x + y = − 7 3 x + 9 y = 27 ​ 10 y = 20 y = 10 20 ​ y = 2
x + 3 y = 9 x = 9 − 3 y x = 9 − 3.2 x = 3
S = { 3 , 2 }
One solution.

Answered by 452 | 2024-06-10

x + 3 y = 9 3 x − y = 7 / ⋅ 3 x + 3 y = 9 9 x − 3 y = 21 10 x = 30 / : 10 x = 3 x + 3 y = 9 3 + 3 y = 9 3 y = 6 y = 2 o n e so l u t i o n − ( 3 ; 2 )

Answered by tomek1172 | 2024-06-10

The system of equations has one and only one solution, which is ( x , y ) = ( 3 , 2 ) . This occurs because the two lines intersect at a single point. Thus, the equations are consistent and independent.
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Answered by 452 | 2024-12-24