 # Investigate for consistency of the following equations and if possible then find the solutions: 2x-3y+7z=5 3x+y-3z=13 2x+19y-47z=32 Dolly Robinson 2020-12-09 Answered
Investigate for consistency of the following equations and if possible then find the solutions:
2x-3y+7z=5
3x+y-3z=13
2x+19y-47z=32
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it Anonym
Step 1
Since you have asked multiple question, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.
Consider the following system of linear equations:
2x−3y+7z=5
3x+y−3z=13
2x+19y−47z=32
Rewrite the system of equations in augmented matrix form:
$\left[\begin{array}{cccc}2& -3& 7& 5\\ 3& 1& -3& 13\\ 2& 19& -47& 32\end{array}\right]$
Step 2
$D=|\begin{array}{ccc}2& -3& 7\\ 3& 1& -3\\ 2& 19& -47\end{array}|$
$=2|\begin{array}{cc}1& -3\\ 19& -47\end{array}|-\left(-3\right)|\begin{array}{cc}3& -3\\ 2& -47\end{array}|+7|\begin{array}{cc}3& 1\\ 2& 19\end{array}|$
$=2\left[1×\left(-47\right)-\left(-3\right)×19\right]+3\left[3×\left(-47\right)-\left(-3\right)×2\right]+7\left(3×19-1×2\right)$
=2(-47+57)+3(-141+6)+7(57-2)
$=2×10+3×\left(-135\right)+7×55$
D=20 - 405 + 385
=0
Step 3
${D}_{x}=|\begin{array}{ccc}5& -3& 7\\ 13& 1& -3\\ 32& 19& -47\end{array}|$
$=5|\begin{array}{cc}1& -3\\ 19& -47\end{array}|-\left(-3\right)|\begin{array}{cc}13& -3\\ 32& -47\end{array}|+7|\begin{array}{cc}13& 1\\ 32& 19\end{array}|$
$=5\left[1×\left(-47\right)-\left(-3\right)×19\right]+3\left[13×\left(-47\right)-\left(-3\right)×32\right]+7\left(13×19-1×32\right)$
=5(-47+57)+3(-611+96)+7(247-32)
$=5×10+3×\left(-515\right)+7×215$
${D}_{x}=50-1545+1505$
=10
D=0 and ${D}_{x}\ne 0$.
Hence, the system of equations is inconsistent.
Hence, the system of equations has no solution.
###### Not exactly what you’re looking for? Jeffrey Jordon