Cem Hayes

2021-01-22

Given the system of equation below , identify the number of solutions.

$\{\begin{array}{l}y=5x-7\\ 15x-3y=7\end{array}$

2k1enyvp

Skilled2021-01-23Added 94 answers

Step 1

Solve the system of equations, using matrices. Given matrix reduced into row-echelon form.

Step 2

Given system of equations

(1)$y=5x-7$

(2)$15x-3y=7$

(3)$\{\begin{array}{l}y=5x-7\\ 15x-3y=7\end{array}$

(3) can be written in matrix form Ax=b

$\Rightarrow \left[\begin{array}{cc}5& -1\\ 15& -3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}7\\ 7\end{array}\right]$

Agumented matrix$\left[\begin{array}{c}{}^{A}{/}_{b}\end{array}\right]=\left[\begin{array}{ccc}5-1& |& 7\\ 15-3& |& 7\end{array}\right]$

Reduced into row echelon form

${R}_{2}\to {R}_{2}-3{R}_{1}$

$\left[\begin{array}{cccc}5& -1& |& 7\\ 0& 0& |& 7\end{array}\right]$

$\therefore P(A)=1,P{(}^{A}{/}_{B})=2$

$\therefore P(A)\ne P{(}^{A}{/}_{B})$

Thus the system of equation have no solution

Ans:No solution

Solve the system of equations, using matrices. Given matrix reduced into row-echelon form.

Step 2

Given system of equations

(1)

(2)

(3)

(3) can be written in matrix form Ax=b

Agumented matrix

Reduced into row echelon form

Thus the system of equation have no solution

Ans:No solution

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

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