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

The answers are:

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

For the second equation we have:

Then, substituting y into the first equation:

Then, substituting x into the second equation:

So, for the system A, we have:

x= 5

y= 2

Substituting y into the first equation we have:

Substituting x into the second equation, we have:

So, for the system B, we have:

x= -1

y= -2

Dividing the second equation by three, we have:

Substituting y into the first equation, we have:

Substituting x into the second equation, we have:

So, for the system C, we have:

x=5

y=2

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!

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation:

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w