Question

\begin{aligned}
&y=4x -5
\\\\
&y=2x +3
\end{aligned}

Answer 1

You have two equations:

1. \( y = 4x - 5 \) (Equation 1)
2. \( y = 2x + 3 \) (Equation 2)

To find the point of intersection of these two lines (if they intersect), we can set the two equations equal to each other:

\[
4x - 5 = 2x + 3
\]

Now, let's solve for \( x \):

1. Subtract \( 2x \) from both sides:
\[
4x - 2x - 5 = 3
\]
This simplifies to:
\[
2x - 5 = 3
\]

2. Add 5 to both sides:
\[
2x = 8
\]

3. Divide by 2:
\[
x = 4
\]

Now that we have the value of \( x \), we can substitute it back into either of the original equations to find the corresponding \( y \). We'll use Equation 1:

\[
y = 4(4) - 5 = 16 - 5 = 11
\]

Thus, the point of intersection is:

\[
\boxed{(4, 11)}
\]