Use the substitution or elimination method to solve each system o...

Question

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 
2x + 6y = 6 
5x + 9y = 9

Accepted Answer

Hello everybody. I have everything right today today we're going to be looking at this math question that states solve the given system of linear equations using the substitution method. Now, the equations include or X plus Y equals 16 N six, X plus five, Y equals 10. Now the answers provided are a five comma negative four B five, comma four C no solution or D infinitely many solutions. So we're looking at this question and specifically using the substitution method, we have to see what, what that entails. So what that entails is basically we're going to be solving for one of the variables in one of the equations and using that solution to plug that in and substitute it into the other equation and continue to solve from there. So in this case, and I'll just label four X plus Y equals to as equation one, N six, X plus five, Y equals 10 as equation two. So in this case, I'm going to be solving for Y using equation one. So we have four X plus Y equals 16, which means that Y is equal to 16 minus four X. Now we can plug this into equation two. So we have equation two which was six X plus five, Y equals 10. And now we can rewrite that as six X plus five. And instead of being five multiply A Y, we'll have five multiplying 16 minus four X. Since that's the solution we obtained for Y with equation one, now we're substituting it into this Y and that will continue to be equal to 10. So once we distribute the five, we can have six X plus five, multiplying a 16 which is 80 and then five multiplying the negative four X which is minus 20 X and that'll be equal to 10. So we have six X plus 80 minus 20 X equals 10. So we can do some rearranging have all the variables on one side, all the numbers on the other side. So I'll keep the variables on the left hand side. So I'll have six X minus 20 X equals and I'll move the 80 over from the left hand side to the right hand side, which means on the right hand side, we'll have 10 minus 80. And now we have six A X minus 20 X which is negative 14, X equals 10 minus 80 which is negative which means that X is equal to positive five after dividing both sides by negative 14. And that's our answer for X. Now we can plug this back into our Y equation. So we had that Y is equal to 16 minus four X. And now we can substitute the X. So we'll have Y equals 16 minus four, multiplying five. Since that's our value for X, which means Y is equal to 16 minus negative four times five is negative 20. So it'll be minus 20. And now we can simplify that 60 minus 20 is negative four. So we have Y equals negative four. So we'll have, we can look at our answer choices and we see that answer choice. A has the order pair five comma negative four. Therefore, answer choice A will be your answer. So I hope that was helpful. And until next time.

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary. 2x + 6y = 6 5x + 9y = 9

Key Concepts

Systems of Equations

Substitution Method

Elimination Method

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