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

N46
Is (1,8) a solution to this system of equations?
y=x+7
y=4x+4

1 answer

To determine if the point (1, 8) is a solution to the system of equations given by:

  1. \( y = x + 7 \)
  2. \( y = 4x + 4 \)

we need to substitute \( x = 1 \) and \( y = 8 \) into both equations and see if both equations are satisfied.

  1. For the first equation: \[ y = x + 7 \] Substituting \( x = 1 \): \[ y = 1 + 7 = 8 \] Since \( y = 8 \) is true, the point (1, 8) satisfies the first equation.

  2. For the second equation: \[ y = 4x + 4 \] Substituting \( x = 1 \): \[ y = 4(1) + 4 = 4 + 4 = 8 \] Since \( y = 8 \) is also true, the point (1, 8) satisfies the second equation as well.

Since (1, 8) satisfies both equations, it is indeed a solution to the system of equations.