Find the solution to the system of equations by graphing
Y=6 - c and y=x - 2
To graph the system of equations, we will create a graph for each equation and see where they intersect.
1) Start with the equation y = 6 - c:
To graph this equation, we need to remember that the y-intercept is 6. Therefore, plot a point at (0, 6) on the graph. From this point, we can find another point by following the slope of -1. This means that for every increase of 1 in x, y decreases by 1.
2) Now, look at the equation y = x - 2:
Again, we find that the y-intercept is -2. Plot a point at (0, -2) on the graph. From this point, follow the slope of 1 to find another point. This means for every increase of 1 in x, y increases by 1.
3) Plot these two points on a graph and draw a line passing through them. The point at which the lines intersect is the solution to the system of equations.
(Note: I apologize for the confusion regarding the variable "c" in the first equation. It is not clear if it is meant to be a variable or a constant. I have treated it as a constant for the purpose of graphing.)
Here is a visual representation of the graphed equations:
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7 | .
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6 | .
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5 | .
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4 | .
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3 | .
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2 | .
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1 | .
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0 |_____________________________________
0 1 2 3 4 5 6 7 8
As seen from the graph, the lines intersect at the point (4, 2). Therefore, the solution to the system of equations is x = 4 and y = 2.
To find the solution to the system of equations by graphing, we need to graph both equations on the same coordinate plane and find the point(s) of intersection.
The first equation is y = 6 - c. Let's graph it:
1. Start by choosing some values for c and finding the corresponding y-values.
For example, if we let c = 0, then y = 6 - 0 = 6. So one point on the graph is (0, 6).
If we let c = 1, then y = 6 - 1 = 5. So another point on the graph is (1, 5).
2. Plot these points on the coordinate plane and draw a straight line passing through them. This line represents the graph of y = 6 - c.
Now, let's move on to the second equation, y = x - 2. We will graph it in the same way:
1. Choose some values for x, and find the corresponding y-values.
For example, if we let x = 0, then y = 0 - 2 = -2. So one point on the graph is (0, -2).
If we let x = 1, then y = 1 - 2 = -1. So another point on the graph is (1, -1).
2. Plot these points on the coordinate plane and draw a straight line passing through them. This line represents the graph of y = x - 2.
Now that we have both lines graphed, we can find the point(s) of intersection by looking for the coordinates where the two lines intersect.