Question

GG.1 Is (x, y) a solution to the system of equations?
N46
Is (4,10) a solution to this system of equations?
y=2x+2
y=10x+1

Answer 1

To determine if the point \((4, 10)\) is a solution to the system of equations, we need to check if it satisfies both equations:

1. \( y = 2x + 2 \)
2. \( y = 10x + 1 \)

**First equation:**
Substitute \(x = 4\) and \(y = 10\) into the first equation:

\[
10 = 2(4) + 2
\]
\[
10 = 8 + 2
\]
\[
10 = 10
\]

This equation is satisfied.

**Second equation:**
Now substitute \(x = 4\) and \(y = 10\) into the second equation:

\[
10 = 10(4) + 1
\]
\[
10 = 40 + 1
\]
\[
10 = 41
\]

This equation is not satisfied.

Since \((4, 10)\) satisfies the first equation but not the second one, we conclude that \((4, 10)\) is **not** a solution to the system of equations.