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

N46
Is (
–
6,8) a solution to this system of equations?
y=8
7x+4y=
–
10

1 answer

To determine if the point \((-6, 8)\) is a solution to the system of equations, we need to check whether this point satisfies both equations.

  1. The first equation is: \[ y = 8 \] Plugging in \(y = 8\): \[ 8 = 8 \] This is true, so the point satisfies the first equation.

  2. The second equation is: \[ 7x + 4y = -10 \] Plugging in \(x = -6\) and \(y = 8\): \[ 7(-6) + 4(8) = -10 \] Calculating the left-hand side: \[ -42 + 32 = -10 \] This simplifies to: \[ -10 = -10 \] This is also true.

Since the point \((-6, 8)\) satisfies both equations, it is a solution to the system of equations.