Question

Select ALL the correct answers.

Select all the statements that are true for the following systems of equations.
System A System B System C
2x - 3y = 4 3x - 4y = 5 2x - 3y = 4
4x - y = 18 y = 5x + 3 12x - 3y = 54

Systems A and B have different solutions.

Systems B and C have the same solution.

System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three.

Systems A and C have the same solution.

All three systems have different solutions

Answer 1

c

Explanation:

Answer 2

Hello!

The answers are:

• A and B have different solutions.

• System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three.

• Systems A and C have the same solution.

Why?

Let's solve each equation system in order to be able to choose the correct statements:

System A

`2x-3y=4\\4x-y=18`

For the second equation we have:

`y=4x-18`

Then, substituting y into the first equation:

`2x-3(4x-18)=4\\2x-12x+54=4\\-10x=4-54\\-10x=-50\\x=5`

Then, substituting x into the second equation:

`y=4(5)-18=2`

So, for the system A, we have:

x= 5

y= 2

System B

`3x-4y=5\\y=5x+3`

Substituting y into the first equation we have:

`3x-4(5x+3)=5\\3x-20x-12=5\\-17x-12=5\\-17x=12+5\\-17x=17\\x=-1`

Substituting x into the second equation, we have:

`y=5(-1)+3=-2`

So, for the system B, we have:

x= -1

y= -2

System C

`2x-3y=4\\12x-3y=54`

Dividing the second equation by three, we have:

`4x-y=18\\y=4x-18`

Substituting y into the first equation, we have:

`2x-3(4x-18)=4\\2x-12x+54=4\\-10x=4-54\\-10x=-50\\x=5`

Substituting x into the second equation, we have:

`y=4(5)-18=2`

So, for the system C, we have:

x=5

y=2

Conclusions

System A and B have different solutions, since:

System A: X=5 and Y=2

System B: X=-1 and Y=-2

System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three, since:

We did the simplification when we were solving the System C:

3(4x-y-18)=12x-3y-54=0

12x-3y=54

System A and C have the same solution, since:

System A: X=5 and Y=2

System C: X=5 and Y=2

Have a nice day!