which statements about this system of equations are true? check all that apply. -x + 6y = 16 8x - 6y = -2…

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 -8x = 14. x = 2 y = 3 there is only one solution to the system of equations.

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 -8x = 14. x = 2 y = 3 there is only one solution to the system of equations.

Answer

Explanation:

Step1: Add the two equations

Add $-x + 6y=16$ and $8x-6y=-2$. $(-x + 6y)+(8x-6y)=16+( - 2)$.

Step2: Simplify the left - hand side

Combine like terms: $(-x+8x)+(6y - 6y)=7x+0 = 7x$.

Step3: Simplify the right - hand side

$16+( - 2)=14$. So the sum of the equations is $7x = 14$, then $x = 2$.

Step4: Substitute $x = 2$ into the first equation

Substitute $x = 2$ into $-x+6y=16$, we get $-2 + 6y=16$. Add 2 to both sides: $6y=18$, then $y = 3$. Since we have found unique values for $x$ and $y$, there is only one solution to the system of equations. Also, when adding the equations, the $y$ - variable is eliminated because $6y+( - 6y)=0$.

Answer:

The y - variable will be eliminated when adding the system of equations. $x = 2$ $y = 3$ There is only one solution to the system of equations.