Use the image to answer the question.
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 (
).
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The intersection point is (5, -1).
The intersection point is (5, -1).
To find the solution to both equations, we need to find the coordinates of the intersection point where the two lines meet.
The first equation is given as y = x - 6, which represents a straight line on the coordinate plane. It has a slope of 1 and a y-intercept of -6.
The second equation is given as y = -x + 4, which also represents a straight line. It has a slope of -1 and a y-intercept of 4.
To find the intersection point, we set the two equations equal to each other:
x - 6 = -x + 4
Now we can solve for x:
2x = 10
x = 5
Now, we can substitute this value of x back into one of the equations to find the corresponding y-coordinate. Let's use the first equation:
y = x - 6
y = 5 - 6
y = -1
So, the intersection point of both lines is (5, -1), as mentioned in the question.