Answer:
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
Step-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
is 5 times
, which means
, so we have
. This means that
So, substituting this back gives