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:The true statements are:The y-variable will be eliminated when adding the system of equationsThere is only one solution to the system of equations isStep-by-step 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