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  • Examine the consistency of the system of equations 2x - y = 5 , x + y = 4.

Q : 2     Examine the consistency of the system of equations

            \small 2x-y=5​​​​​​                                                        

            \small x+y=4

Answers (1)

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We have given the system of equations:

                                        \small 2x-y=5                                            

                                         \small x+y=4

The given system of equations can be written in the form of matrix; AX =B

where A= \begin{bmatrix} 2 &-1 \\ 1&1 \end{bmatrix},  X= \begin{bmatrix} x\\y \end{bmatrix}  and B = \begin{bmatrix} 5\\4 \end{bmatrix}.

So, we want to check for the consistency of the equations;

|A| = 2(1) -1(-1) = 3 \neq 0

Here A is non -singular therefore there exists A^{-1}.

Hence, the given system of equations is consistent.

 

Posted by

Divya Prakash Singh

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