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GG.1 Is (x, y) a solution to the system of equations?

N46
Is (
–
5,6) a solution to this system of equations?
15x+14y=9
18x+18y=18

1 answer

To determine if \( (-5, 6) \) is a solution to the system of equations, we need to substitute \( x = -5 \) and \( y = 6 \) into both equations and check if they are true.

  1. The first equation is:
    \[ 15x + 14y = 9 \] Substituting \( x = -5 \) and \( y = 6 \): \[ 15(-5) + 14(6) = -75 + 84 = 9 \] This equation holds true.

  2. The second equation is: \[ 18x + 18y = 18 \] Again substituting \( x = -5 \) and \( y = 6 \): \[ 18(-5) + 18(6) = -90 + 108 = 18 \] This equation also holds true.

Since \( (-5, 6) \) satisfies both equations, it is indeed a solution to the system of equations.