Use the image to answer the question. Review the graphs of a system of these two linear equations in two variables: y=-x+4 and y=3x. Find the intersection point.

Answer 1

To find the intersection point of the equations \( y = -x + 4 \) and \( y = 3x \), we can set the two equations equal to each other:

\[ -x + 4 = 3x \]

Next, we solve for \( x \):

1. Add \( x \) to both sides: \[ 4 = 4x \]

2. Divide by 4: \[ x = 1 \]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). Using \( y = 3x \):

\[ y = 3(1) = 3 \]

Therefore, the intersection point of the two lines is:

\[ \boxed{(1, 3)} \]