Question

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

Answer 1

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.