Question

Given the system of equations 2x - 8y = 0 and -2x + 4y = -8, which statements are true? Check all that apply.

The x-variable will cancel when adding the system of equations.

After adding the system of equations, you get - 12y = -8.

y = 2

O x = 8

The solution to the system is (2,8).

Answer 1

A.The x- variable will cancel when adding the system of equations

C.y=2

D.x=8

Explanation:

We are given that system of equations

`2x-8y=0`

`-2x+4y=-8`

We have to find the true statements.

Adding two equations then, we get

`-4y=-8`

`y=(-8)/(-4)=2`

Using division property of equality

Substitute y=2 in equation first

`2x-8(2)=0`

`2x-16=0`

`2x=16`

`x=(16)/(2)=8`

Hence, the solution of the system is (8,2).

Option A,C and D are true.

Answer 2

Statement 1,3 and 4 are true.

Explanation:

Given : The system of equations
`2x-8y=0` and
`-2x+4y=-8`

To find : Which statements are true? Check all that apply.

Solution :

Equation 1 -
`2x-8y=0`

Equation 2 -
`-2x+4y=-8`

Solving equations,

Add equation (1) and (2),

Step 1 -
`2x-8y+(-2x+4y)=0+(-8)`

Step 2 -
`2x-8y-2x+4y=0-8`

Step 3 -
`-4y=-8`

Step 4 -
`y=2`

Step 5 - Substitute in equation (1),

`2x-8(2)=0`

`2x=16`

`x=8`

Step 6 - The solution to the system is (8,2).

Statement 1 - The x-variable will cancel when adding the system of equations.

It is true shown in step 2.

Statement 2 - After adding the system of equations, you get - 12y = -8.

It is false shown in step 3.

Statement 3 - y=2

It is true shown in step 4.

Statement 4 - x=8

It is true shown in step 5.

Statement 5 - The solution to the system is (2,8).

It is false shown in step 6.