Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Question 1.
5x+2y=-7
15x+6y=21
No solution, One solution, or infinite solution?

Question 2.
Y=2x+1
2x-4=1
No solution, one solution, or infinite solution?

Question 3.
6x+4y=10
3x+2y=5
No solution, one solution, or infinite solution?

Sagot :

YujiC

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

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.