Is (5,10) a solution to this system of equations?

Question

15x–6y=15
20x–12y=
–
20

Answer 1

To determine whether \((5, 10)\) is a solution to the given system of equations, we need to substitute \(x = 5\) and \(y = 10\) into both equations and see if they hold true.

1. First, let's check the first equation: \[ 15x - 6y = 15 \] Substitute \(x = 5\) and \(y = 10\): \[ 15(5) - 6(10) = 15 \] \[ 75 - 60 = 15 \] \[ 15 = 15 \] This equation is true.

2. Next, let's check the second equation: \[ 20x - 12y = -20 \] Substitute \(x = 5\) and \(y = 10\): \[ 20(5) - 12(10) = -20 \] \[ 100 - 120 = -20 \] \[ -20 = -20 \] This equation is also true.

Since both equations hold true with the substitutions, \((5, 10)\) is indeed a solution to the system of equations.