Question

Which statements about this system of equations are true? Check all that apply. - x + 6y = 16 8x - 6y = -2 The x-variable will be eliminated when adding the system of equations. The y-variable will be eliminated when adding the system of equations. The sum of the system of equations is - x + 6yThere is only one solution to the system of equations.

Answer 1

B, D, E, and F

Explanation:

Took the test

Answer 2

The true statements are:

The y-variable will be eliminated when adding the system of equations

There is only one solution to the system of equations is

Explanation:

* Lets explain how to solve the problem

- We use the elimination method to solve the system of the

linear equation

- The solution is one of three cases

# Exactly one solution ⇒ the 2 lines which represented the equations

intersect each other at one point

# No solution ⇒ the 2 lines which represented the equations are

parallel to each other

# Infinite solutions ⇒ the two lines are coincide

- In the system of the linear equations of the problem we have two

linear equations -x + 6y = 16 and 8x - 6y = -2

- To solve we must to eliminate one of the two variables

∵ The y's in the two equations have the same coefficients and

different signs

∴ We add the equations to eliminate y

∴ (-x + 8x) + (6y - 6y) = 16 + -2

∴ 7x = 14 ⇒ divide both sides by 7

∴ x = 2

- Substitute the x in any one of the two equations by 2

∴ -2 + 6y = 16 ⇒ add 2 to both sides

∴ 6y = 18 ⇒ divide both sides by 6

∴ y = 3

∴ The solution of the system of the equations is (2 , 3) ⇒ only one

solution

- Lets check the statements to find the true statements

# The x-variable will be eliminated when adding the system of

equations is not true

# The y-variable will be eliminated when adding the system of

equations is true

# The sum of the system of equations is - x + 6y is not true

# There is only one solution to the system of equations is true