Question

1. x+2y = 22x+3y = 3

Answer 1

The given system of equations is,

x+2y=2 and 2x+3y=3

Write the system of equations in the form of AX=B.

[ 1 2 2 3 ][ x y ]=[ 2 3 ]

Here, A=[ 1 2 2 3 ], X=[ x y ] and B=[ 2 3 ].

Now, the determinant of A is,

| A |=1×3−2×2 =3−4 =−1

Since, | A |≠0. Therefore, inverse of matrix A exists.

Hence, the system of equations is consistent.