The system of equations is shown by the graph.
y = 25x + 200
y = 50x + 75
The solution to the system is ( __, __ ).
What is the solution to the system of equations shown by the graph?
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The system of equations is shown by the graph.
y = 25x + 200
y = 50x + 75
The solution to the system is ( __, __ ).
To find the solution to the system of equations given by the lines ( y = 25x + 200 ) and ( y = 50x + 75 ), you need to find the point where the two lines intersect.
1. Set the equations equal to each other because at the intersection, both expressions for ( y ) will be equal:
[
25x + 200 = 50x + 75
]
2. Rearrange the equation to isolate ( x ):
[
200 – 75 = 50x – 25x
]
[
125 = 25x
]
3. Solve for ( x ):
[
x = frac{125}{25} = 5
]
4. Substitute ( x ) back into one of the original equations to find ( y ). Using the first equation:
[
y = 25(5) + 200 = 125 + 200 = 325
]
Thus, the solution to the system of equations is ( (5, 325) ).
So, the answer is (5, 325).