Question

For example, if I say, 2 , 5 , (2,5) is a solution to the equation "y" equals 2 "x" plus 3y=2x+3," how could you check my claim

Answer 1

To check whether the point (2, 5) is a solution to the equation \( y = 2x + 3 \), we need to substitute \( x = 2 \) and \( y = 5 \) into the equation and see if both sides of the equation are equal.

1. Start with the equation:
\[
y = 2x + 3
\]

2. Substitute \( x = 2 \) into the equation:
\[
y = 2(2) + 3
\]
\[
y = 4 + 3
\]
\[
y = 7
\]

3. Now, we compare the calculated value of \( y \) with the given \( y \)-value:
- You provided \( y = 5 \), but our calculation gives \( y = 7 \).

Since \( 5 \neq 7 \), the point \( (2, 5) \) is **not** a solution to the equation \( y = 2x + 3 \).

To verify, the correct substitution would show that for \( x = 2 \), \( y \) should equal 7, not 5. Thus, your claim is incorrect.