Answer:
The system of equations i.e. y - x = 15 and 25 + 2x = y represents the correct graph as the point of intersection of this system is (x, y) = (-10, 5) which is also the point of intersection of the two lines shown in graph.
Step-by-step explanation:
The graph is showing the following system of equations:
y - x = 15 and 25 + 2x = y
The reason is very simple. As the point of intersection of two lines is (-10, 5). It means the two lines in the graph meet at the x-coordinate = -10 and y-coordinate = 5. So, (-10, 5) is the point of intersection of the two lines as shown graph.
If we solve the system of equations i.e. y - x = 15 and 25 + 2x = y to get the values of x and y to determine its intersection. So, we would get the value of x = -10, and y = 5. Hence, The graph is showing the system of the equation of y - x = 15 and 25 + 2x = y.
<em>Verification: Lets solve </em>system of equations i.e. y - x = 15 and 25 + 2x = y to get the values of x and y to determine its intersection.
y - x = 15
y = x + 15
Substitute x+15 for y in 2x+25 = y
2x + 25 = y
2x + 25 = x + 15
x = −10
Substitute x = −10 for x in y = x+15
y = x + 15
y = −10 + 15
y = 5
So, x = −10 and y = 5
Hence, The graph is showing the system of the equations of y - x = 15 and 25 + 2x = y.
<em>The system of equation in first choice (y=15 and y =25), represent a pair of parallel lines which will never intersect at any point, and two other system of equations in the given options yield different point of intersections. Hence, they do not represent the corresponding graph.</em>
Therefore, only the system of equations i.e. y - x = 15 and 25 + 2x = y represents the correct graph as the point of intersection of this system is (x, y) = (-10, 5) which is also the point of intersection of the two lines shown in graph.
Keywords: system of equation, point of intersection, graph
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