Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows 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 7. The equation of the dotted line is y equals 4 x minus 3. The lines intersect at left parenthesis 2 comma 5 right parenthesis which is not plotted as a point.
Estimate the intersection point of the graphs of the following linear equations in two variables.
y=−x+7
y=4x−3
(1 point)
(
)
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The intersection point of the graphs of the two linear equations y = -x + 7 and y = 4x - 3 is estimated to be approximately (2, 5).
To estimate the intersection point of the graphs of the linear equations y = -x + 7 and y = 4x - 3, we can visually analyze the graph provided.
Looking at the graph, we can see that the solid line represents y = -x + 7, and the dotted line represents y = 4x - 3. The point where these two lines intersect is the intersection point.
From the graph, it appears that the lines intersect at the point (2, 5).
Therefore, we can estimate that the intersection point of the graphs of the given linear equations is (2, 5).
To estimate the intersection point of the graphs of the given linear equations, we can substitute the equations into each other and solve for the variables.
1. Substitute the equation "y = -x + 7" into the second equation "y = 4x - 3":
-x + 7 = 4x - 3
2. Simplify this equation by adding x to both sides:
7 = 5x - 3
3. Add 3 to both sides:
10 = 5x
4. Divide both sides by 5 to solve for x:
x = 2
5. Substitute the value of x back into one of the equations (for example, "y = -x + 7"):
y = -2 + 7
y = 5
Hence, the estimated intersection point of the graphs of the given linear equations is (2, 5).