Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Answer:
Q1: no solution
Q2: one solution
Q3: infinite solutions
Step-by-step explanation:
Question 1
Answer: No solution
-------------------
Explanation:
Multiply both sides of the first equation by 3. Doing so leads to
3*(5x+2y) = 3*(-7)
15x+6y = -21
The second equation is 15x+6y = 21
Let's say we let z = 15x+6y
This means the system
[tex]\begin{cases}15x+6y = -21\\15x+6y = 21\end{cases}[/tex]
becomes
[tex]\begin{cases}z = -21\\z = 21\end{cases}[/tex]
but we can't have z be equal to more than one value at a time. We have a contradiction and therefore there are no solutions.
===============================================
Question 2
Answer: One solution
The solution is (x,y) = (5/6)
-------------------
Explanation:
Apply substitution
2x - 4y = 1
2x - 4(2x+1) = 1
2x - 8x - 4 = 1
-6x - 4 = 1
6x = 1+4
6x = 5
x = 5/6
Then use this to find y
y = 2x+1
y = 2(5/6)+1
y = 5/3 + 1
y = 5/3 + 3/3
y = 8/3
The one solution is (x,y) = (5/6)
===============================================
Question 3
Answer: Infinitely many solutions
-------------------
Explanation:
Multiply both sides of the second equation by 2
3x+2y = 5 becomes 2*(3x+2y) = 2*5 which turns into 6x+4y = 10
This is exactly identical to the first equation of the original system given.
So both equations represent the same thing. We have infinitely many intersection points, and infinitely many solutions.
All of these solutions are on the line 3x+2y = 5
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
