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

N46
Is (2,9) a solution to this system of equations?
y=3x+3
y=x+5

1 answer

To determine if the point (2, 9) is a solution to the system of equations given by:

  1. \( y = 3x + 3 \)
  2. \( y = x + 5 \)

we need to substitute \( x = 2 \) and \( y = 9 \) into both equations.

For the first equation:

\[ y = 3x + 3 \]

Substituting \( x = 2 \):

\[ y = 3(2) + 3 = 6 + 3 = 9 \]

So, \((2, 9)\) satisfies the first equation.

For the second equation:

\[ y = x + 5 \]

Substituting \( x = 2 \):

\[ y = 2 + 5 = 7 \]

So, \((2, 9)\) does not satisfy the second equation.

Since (2, 9) satisfies the first equation but not the second one, it is not a solution to the system of equations.