To find the intersection point of the equations \( y = 4x - 3 \) and \( y = -x + 7 \), we can set the two equations equal to each other since at the intersection the \( y \) values will be the same:
\[ 4x - 3 = -x + 7 \]
Now, solve for \( x \):
- Add \( x \) to both sides:
\[ 4x + x - 3 = 7 \]
This simplifies to:
\[ 5x - 3 = 7 \]
- Add \( 3 \) to both sides:
\[ 5x = 10 \]
- Divide by \( 5 \):
\[ x = 2 \]
Now, substitute \( x = 2 \) back into one of the original equations to find \( y \). Using \( y = 4x - 3 \):
\[ y = 4(2) - 3 = 8 - 3 = 5 \]
Thus, the intersection point is \( (2, 5) \).
In the format you provided, it would be represented as:
(2, 5)