A coordinate plane with four quadrants shows the x-axis ranging from negative 5 to 15 in increments of 1, and the y-axis ranging from negative 10 to 10 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals x minus 6. The equation of the dotted line is y equals negative x plus 4. The intersection point of both lines is shown at positive 5 on the x-axis and negative 1 on the y-axis in quadrant 4.

Question

Review the graphs of a system of two linear equations in two variables: y=x−6
and y=−x+4
. Find the solution to both equations.

(1 point)
The intersection point is (
).

Answer 1

To find the intersection point of the two equations \( y = x - 6 \) and \( y = -x + 4 \), we can set them equal to each other:

\[ x - 6 = -x + 4 \]

Next, we will solve for \( x \):

1. Add \( x \) to both sides:

\[ x + x - 6 = 4 \]

2. Combine like terms:

\[ 2x - 6 = 4 \]

3. Add 6 to both sides:

\[ 2x = 10 \]

4. Divide by 2:

\[ x = 5 \]

Now, we can substitute \( x = 5 \) back into either of the original equations to find \( y \). We can use the first equation:

\[ y = 5 - 6 = -1 \]

Thus, the intersection point, which is the solution to the system of equations, is:

\[ (5, -1) \]

Therefore, the intersection point is \( (5, -1) \).