How to solve the following system with $xge 0, yge 0$ solutions The Next CEO of Stack OverflowFind range of $x$ satisfying $left lfloor frac3x right rfloor+left lfloor frac4x right rfloor=5$Solve the following system of linear equations for any values of real parameter $a$…Solutions of a system of linear equations with a parameterFinding values of $a$ with which a simple system has exactly 2 solutionsSystem of linear equations with parameter - strange result, does this make senseFind all values of $a$ for which the system of equations it has exactly two solutionsSolve the system $x^2-3xy+2y^2+x-y=0$, $2x^2-2xy-3y^2-2x+5y=0$Solutions of a non-linear system of equationsHow to solve the following system : $ begincases ab^2 = 2 \ a+b = -1 endcases $?Find trivial and non-trivial solutions to a system with a parameterHow to “quickly” solve the following linear system of equations?
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How to solve the following system with $xge 0, yge 0$ solutions
The Next CEO of Stack OverflowFind range of $x$ satisfying $left lfloor frac3x right rfloor+left lfloor frac4x right rfloor=5$Solve the following system of linear equations for any values of real parameter $a$…Solutions of a system of linear equations with a parameterFinding values of $a$ with which a simple system has exactly 2 solutionsSystem of linear equations with parameter - strange result, does this make senseFind all values of $a$ for which the system of equations it has exactly two solutionsSolve the system $x^2-3xy+2y^2+x-y=0$, $2x^2-2xy-3y^2-2x+5y=0$Solutions of a non-linear system of equationsHow to solve the following system : $ begincases ab^2 = 2 \ a+b = -1 endcases $?Find trivial and non-trivial solutions to a system with a parameterHow to “quickly” solve the following linear system of equations?
$begingroup$
Find all the values of the parameter p for which the following system: $$begincasespx + 3y = -p \ 3x+py ; ;= 8 endcases$$ has $x ge 0, yge 0$ solutions.
I got $(-3;8]$ but in answers there is $[-3;0]$. Just added the two equations and got $$x+y=(8-p)/(p+3).$$ Where is the mistake?
algebra-precalculus systems-of-equations
edited Mar 21 at 22:18
Strants
5,74021736
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
$endgroup$
add a comment |
$begingroup$
Find all the values of the parameter p for which the following system: $$begincasespx + 3y = -p \ 3x+py ; ;= 8 endcases$$ has $x ge 0, yge 0$ solutions.
I got $(-3;8]$ but in answers there is $[-3;0]$. Just added the two equations and got $$x+y=(8-p)/(p+3).$$ Where is the mistake?
algebra-precalculus systems-of-equations
edited Mar 21 at 22:18
Strants
5,74021736
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
$endgroup$
$begingroup$
Hint: $p(x+y) + 3(x+y) = 8-p = (x+y) (p+3)$...
$endgroup$
– kelalaka
Mar 18 at 10:11
5
$begingroup$
Dear Sandro, this site has a code of asking questions where "I tried to" is recognized as not being appropriate to show your own efforts. Even if your tries didn't lead to results, you are urged to show us what you did. Thanks.
$endgroup$
– Andreas
Mar 18 at 10:16
add a comment |
$begingroup$
Find all the values of the parameter p for which the following system: $$begincasespx + 3y = -p \ 3x+py ; ;= 8 endcases$$ has $x ge 0, yge 0$ solutions.
I got $(-3;8]$ but in answers there is $[-3;0]$. Just added the two equations and got $$x+y=(8-p)/(p+3).$$ Where is the mistake?
algebra-precalculus systems-of-equations
edited Mar 21 at 22:18
Strants
5,74021736
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
$endgroup$
Find all the values of the parameter p for which the following system: $$begincasespx + 3y = -p \ 3x+py ; ;= 8 endcases$$ has $x ge 0, yge 0$ solutions.
I got $(-3;8]$ but in answers there is $[-3;0]$. Just added the two equations and got $$x+y=(8-p)/(p+3).$$ Where is the mistake?
algebra-precalculus systems-of-equations
algebra-precalculus systems-of-equations
edited Mar 21 at 22:18
Strants
5,74021736
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
edited Mar 21 at 22:18
Strants
5,74021736
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
edited Mar 21 at 22:18
Strants
5,74021736
edited Mar 21 at 22:18
Strants
5,74021736
edited Mar 21 at 22:18
Strants
5,74021736
5,74021736
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
asked Mar 18 at 10:01
Sandro JologuaSandro Jologua
95
95
$begingroup$
Hint: $p(x+y) + 3(x+y) = 8-p = (x+y) (p+3)$...
$endgroup$
– kelalaka
Mar 18 at 10:11
5
$begingroup$
Dear Sandro, this site has a code of asking questions where "I tried to" is recognized as not being appropriate to show your own efforts. Even if your tries didn't lead to results, you are urged to show us what you did. Thanks.
$endgroup$
– Andreas
Mar 18 at 10:16
add a comment |
$begingroup$
Hint: $p(x+y) + 3(x+y) = 8-p = (x+y) (p+3)$...
$endgroup$
– kelalaka
Mar 18 at 10:11
5
$begingroup$
Dear Sandro, this site has a code of asking questions where "I tried to" is recognized as not being appropriate to show your own efforts. Even if your tries didn't lead to results, you are urged to show us what you did. Thanks.
$endgroup$
– Andreas
Mar 18 at 10:16
$begingroup$
Hint: $p(x+y) + 3(x+y) = 8-p = (x+y) (p+3)$...
$endgroup$
– kelalaka
Mar 18 at 10:11
$begingroup$
Hint: $p(x+y) + 3(x+y) = 8-p = (x+y) (p+3)$...
$endgroup$
– kelalaka
Mar 18 at 10:11
5
5
$begingroup$
Dear Sandro, this site has a code of asking questions where "I tried to" is recognized as not being appropriate to show your own efforts. Even if your tries didn't lead to results, you are urged to show us what you did. Thanks.
$endgroup$
– Andreas
Mar 18 at 10:16
$begingroup$
Dear Sandro, this site has a code of asking questions where "I tried to" is recognized as not being appropriate to show your own efforts. Even if your tries didn't lead to results, you are urged to show us what you did. Thanks.
$endgroup$
– Andreas
Mar 18 at 10:16
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Hint:
By Gaussian elimination,
$$(p^2-9)x=-p^2-24,\(p^2-9)y=11p.$$
Now solve the inequations.
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
Hint
By using Cramer's rule we have $$x=beginvmatrix-p&3\8&pendvmatrixover beginvmatrixp&3\3&pendvmatrix\y=beginvmatrixp&-p\3&8endvmatrixover beginvmatrixp&3\3&pendvmatrix$$so what do these lead to?
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
add a comment |
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2 Answers
2
active
oldest
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2 Answers
2
active
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votes
$begingroup$
Hint:
By Gaussian elimination,
$$(p^2-9)x=-p^2-24,\(p^2-9)y=11p.$$
Now solve the inequations.
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
Hint:
By Gaussian elimination,
$$(p^2-9)x=-p^2-24,\(p^2-9)y=11p.$$
Now solve the inequations.
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
$endgroup$
add a comment |
$begingroup$
Hint:
By Gaussian elimination,
$$(p^2-9)x=-p^2-24,\(p^2-9)y=11p.$$
Now solve the inequations.
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
$endgroup$
Hint:
By Gaussian elimination,
$$(p^2-9)x=-p^2-24,\(p^2-9)y=11p.$$
Now solve the inequations.
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
edited Mar 18 at 10:39
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
answered Mar 18 at 10:34
Yves DaoustYves Daoust
131k676229
131k676229
add a comment |
add a comment |
$begingroup$
Hint
By using Cramer's rule we have $$x=beginvmatrix-p&3\8&pendvmatrixover beginvmatrixp&3\3&pendvmatrix\y=beginvmatrixp&-p\3&8endvmatrixover beginvmatrixp&3\3&pendvmatrix$$so what do these lead to?
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
add a comment |
$begingroup$
Hint
By using Cramer's rule we have $$x=beginvmatrix-p&3\8&pendvmatrixover beginvmatrixp&3\3&pendvmatrix\y=beginvmatrixp&-p\3&8endvmatrixover beginvmatrixp&3\3&pendvmatrix$$so what do these lead to?
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
add a comment |
$begingroup$
Hint
By using Cramer's rule we have $$x=beginvmatrix-p&3\8&pendvmatrixover beginvmatrixp&3\3&pendvmatrix\y=beginvmatrixp&-p\3&8endvmatrixover beginvmatrixp&3\3&pendvmatrix$$so what do these lead to?
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
$endgroup$
Hint
By using Cramer's rule we have $$x=beginvmatrix-p&3\8&pendvmatrixover beginvmatrixp&3\3&pendvmatrix\y=beginvmatrixp&-p\3&8endvmatrixover beginvmatrixp&3\3&pendvmatrix$$so what do these lead to?
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
answered Mar 18 at 11:38
Mostafa AyazMostafa Ayaz
18.1k31040
18.1k31040
add a comment |
add a comment |
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$begingroup$
Hint: $p(x+y) + 3(x+y) = 8-p = (x+y) (p+3)$...
$endgroup$
– kelalaka
Mar 18 at 10:11
5
$begingroup$
Dear Sandro, this site has a code of asking questions where "I tried to" is recognized as not being appropriate to show your own efforts. Even if your tries didn't lead to results, you are urged to show us what you did. Thanks.
$endgroup$
– Andreas
Mar 18 at 10:16