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anonymous
 one year ago
its 2 30 AM need to wake up in 3 hours, please help me finish this last question fast
A system of equations is shown below:
3x + 7y = 16
9x + 5y = 16
Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points)
Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)
anonymous
 one year ago
its 2 30 AM need to wake up in 3 hours, please help me finish this last question fast A system of equations is shown below: 3x + 7y = 16 9x + 5y = 16 Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points) Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2if we multiply the first equation by 3, we get: \[9x  21y = 48\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2Now if we sum that equation with the second one, what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: \[9x  21y + \left( {  9x + 5y} \right) = 48 + 16\] please simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but wouldnt that be x16y=16?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2no, since the next step is: \[9x  21y  9x + 5y = 48 + 16\] please simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh you put addition at first, x25y=64

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: what is 9 9 =...

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! so the coefficient of the term with x is zero. Now what is 21 + 5= ...?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! so the coefficient of the term with y is 16

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2then we can write: \[0x  16y = 64\] and finally: \[  16y = 64\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! so the requested system of part A, can be this: \[\left\{ \begin{gathered}  3x + 7y =  16 \hfill \\  16y = 64 \hfill \\ \end{gathered} \right.\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats it for part A?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0perfect, now what do we do for part B?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2we can consider the last system, namely the equivalent system, and we can solve the second equation for y, namely: \[  16y = 64\] what is y?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: divide both sides by 16, what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now substitute that value of y into the first equation of the equivalent system, namely: \[  3x + 7y =  16\] what equation do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2not exactly, here is the right step: \[  3x + 7 \times \left( {  4} \right) =  16\] please simplify

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2what is: \[7 \times \left( {  4} \right) = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: \[7 \times \left( {  4} \right) =  28\] am I right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops lol, yeah you're right, i accidentally multiplied by 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry its real late over here, cant think properly

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! So we have: \[  3x  28 =  16\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now if we add 28 to both sides, we get: \[  3x  28 + 28 =  16 + 28\] please simplify

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! then if we divide both sides by 3, we can write: \[\frac{{  3x}}{{  3}} = \frac{{12}}{{  3}}\] please simplify

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2perfect! So the solution of the equivalent system is: \[\left\{ \begin{gathered} x =  4 \hfill \\ y =  4 \hfill \\ \end{gathered} \right.\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now, please substitute that solution into the first equation of the original system, namely: \[  3x + 7y =  16\] what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: \[  3 \times \left( {  4} \right) + 7 \times \left( {  4} \right) =  16\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2what is (3) * (4)=... and 7*(4)=...?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! so we can write: \[12  28 =  16\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now what is 1228=...?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! So we can write: \[  16 =  16\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thanks a lot! appreciate every thing, you taught me better than any teacher has in school!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2reassuming the solution of the equivalent system makes the first equation an identity

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now we have to do the same procedure for the second equation of the original system. If the solution of the equivalent system makes an identity the second equation of the original system then we can state that the two systems, namely the original system and the equivalent system have the same solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i think we only have to do it with one equation, but i might be wrong

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2so if we substitute the solution of the equivalent system: \[\left\{ \begin{gathered} x =  4 \hfill \\ y =  4 \hfill \\ \end{gathered} \right.\] into the second equation of the original system: \[  9x + 5y = 16\] what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! \[  9 \times \left( {  4} \right) + 5 \times \left( {  4} \right) = 16\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2now please simplify: what is (9)*(4)=...? and 5*(4)=...?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2so we can write: \[36  20 = 16\] now what is 3620=...?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! so we got an identity again!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2then we can state that both systems have the same solution, which is: \[\left\{ \begin{gathered} x =  4 \hfill \\ y =  4 \hfill \\ \end{gathered} \right.\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, thanks for all the help! greatly appreciate it
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