Question

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

Answer 1

Answer:

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

C.y=2

D.x=8

Step-by-step 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

$-4y=-8$

$y=\frac{-8}{-4}=2$

Using division property of equality

Substitute y=2 in equation first

$2x-8(2)=0$

$2x-16=0$

$2x=16$

$x=\frac{16}{2}=8$

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

Option A,C and D are true.

Answer 2

Answer:

Statement 1,3 and 4 are true.

Step-by-step 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.