Solving Systems of Equations by Graphing Practice

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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.

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 (
).
Remaining Attempts : 3
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Answer 1

To find the solution to the system of equations given by the lines \(y = x - 6\) and \(y = -x + 4\), we need to determine the point where these two lines intersect.

From the information provided:

1. The coordinates of the intersection point are given as \( (5, -1) \).
2. We can verify that this point satisfies both equations.

Let's check:

• For the first equation, \(y = x - 6\):

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

This is correct since when \(x = 5\), \(y\) indeed equals \(-1\).

• For the second equation, \(y = -x + 4\):

\[ y = -5 + 4 = -1 \]

This is also correct since when \(x = 5\), \(y\) equals \(-1\) as well.

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

The intersection point is \((5, -1)\).