Is (–2,10) a solution to this system of equations?

Question

y=–4x+2
y=–6x–2
yes or no

Answer 1

To determine if \((-2, 10)\) is a solution to the system of equations, we will substitute \(x = -2\) and \(y = 10\) into both equations and see if the equations hold true.

1. For the first equation \(y = -4x + 2\): \[ 10 = -4(-2) + 2 \] \[ 10 = 8 + 2 \] \[ 10 = 10 \quad \text{(true)} \]

2. For the second equation \(y = -6x - 2\): \[ 10 = -6(-2) - 2 \] \[ 10 = 12 - 2 \] \[ 10 = 10 \quad \text{(true)} \]

Since \((-2, 10)\) satisfies both equations, the answer is yes.