Which statement explains why 13x – 13y=-26 shares a solution with this system of equations: { 10x – 3y = 29
{ -3z + 10y = 55
A:
Because 13x – 13y = -26 is the product of the two equations in the system of equations, it the
must share a solution with the system of equations.
B:
The three equations all have the same slope but different y intercepts. Equations with the same
slope but different y-intercepts always share a solution.
C:
Because 10x – 3y is equal to 29, I can add 10x – 3y to the left side of-3z +10y = 55 and add
29 to the right side of the same equation. Adding equivalent expressions to each side of an
equation does not change the solution to the equation.
D:
Because -3z +10y is equal to 55, I can subtract-3z + 10y from the left side of 102 - 3y= 29
and subtract 55 from its right side Subtracting equivalent expressions from each side of an
equation does not change the solution to the equation.