An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 6. The equation of the dotted line is y equals x plus 2. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.

Question

Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2


y=−x+6


(1 point)
(
,
)

Answer 1

To find the intersection point of the two equations \( y = x + 2 \) and \( y = -x + 6 \), we need to set them equal to each other:

1. Set the equations equal to each other: \[ x + 2 = -x + 6 \]

2. Solve for \( x \):

   • Add \( x \) to both sides: \[ 2x + 2 = 6 \]
   • Subtract 2 from both sides: \[ 2x = 4 \]
   • Divide by 2: \[ x = 2 \]

3. Substitute \( x = 2 \) back into one of the original equations to find \( y \). Using \( y = x + 2 \): \[ y = 2 + 2 = 4 \]

Therefore, the intersection point is \( (2, 4) \).

The estimated intersection point is: \[ \boxed{(2, 4)} \]