Is the equation y=2x+3 true when x=2 and y=7?

Question

You found that x=2, y=7 makes the first equation true. Does x=2, y=7 also make the second equation, y=2x+3, true? Start by substituting 2 for x.
y=3+2x
y=2x+3

y
=
2x
+ 3
y
=
2
⋅
+ 3

Answer 1

To determine if the equation \( y = 2x + 3 \) is true when \( x = 2 \) and \( y = 7 \), we can substitute \( 2 \) for \( x \) in the equation and check if it results in \( y = 7 \).

Start with the equation:

\[ y = 2x + 3 \]

Now, substitute \( x = 2 \):

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

Calculate the right side:

\[ y = 4 + 3 = 7 \]

Since substituting \( x = 2 \) gives us \( y = 7 \), this means that \( (x, y) = (2, 7) \) satisfies the equation \( y = 2x + 3 \).

So yes, when \( x = 2 \) and \( y = 7 \), the equation \( y = 2x + 3 \) is true.