Question

Find an equivalent system of equations for the following system:

3x + 3y = 0
−4x + 4y = −8

3x + 3y = 0
7x − y = 8
3x + 3y = 0
−7x − y = 8
3x + 3y = 0
−7x + 7y = 8
3x + 3y = 0

Answer 1

A and B

Explanation:

An equivalent system of equation is found by adding or subtracting the second equation or when any multiple of both equations are added or subtracted to each other.

Let us see part by part.

A.

Answer 2

`\left \{ {{3x+3y=0} \atop {7x-y=8}} \right.`

Explanation:

An equivalent system refer to other system that has the same values for the variables, or it's satisfied by the same values. First, we calculate what are the values for x and y, in the given system.

`\left \{ {{3x+3y=0} \atop {-4x+4y=-8}} \right.`

Extracting common factors:

`\left \{ {{3(x+y)=0} \atop {4(-x+y)=-8}} \right. \\\left \{ {{x+y=0} \atop {-x+y=-2}} \right.`

Now, summing both equations we have:

`2y=-2\\y=-1`

Replacing this value in a equation we have:

`3x+3y=0\\3x+3(-1)=0\\3x-3=0\\x=(3)/(3)=1`

Now, we have to find the other system that it's satisfied by
`y=-1` and
`1`.

`\left \{ {{3x+3y=0} \atop {7x-y=8}} \right.\\3(1)+3(-1)=0\\3-3=0\\0=0\\7(1)-(-1)=8\\7+1=8\\8=8`

As you can see, the first system is equivalent because it has the same solution as the given system of equations.

Therefore, the correct answer is the first one.