Cem Hayes

2021-01-22

Given the system of equation below , identify the number of solutions.
$\left\{\begin{array}{l}y=5x-7\\ 15x-3y=7\end{array}$

2k1enyvp

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)$\left\{\begin{array}{l}y=5x-7\\ 15x-3y=7\end{array}$
(3) can be written in matrix form Ax=b
$⇒\left[\begin{array}{cc}5& -1\\ 15& -3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}7\\ 7\end{array}\right]$
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
${R}_{2}\to {R}_{2}-3{R}_{1}$
$\left[\begin{array}{cccc}5& -1& |& 7\\ 0& 0& |& 7\end{array}\right]$
$\therefore P\left(A\right)=1,P{\left(}^{A}{/}_{B}\right)=2$
$\therefore P\left(A\right)\ne P{\left(}^{A}{/}_{B}\right)$
Thus the system of equation have no solution
Ans:No solution

Jeffrey Jordon