Solve the system by graphing.
x+y=−2
y=13x+2
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http://www.wolframalpha.com/input/?i=+x%2By%3D%E2%88%922+%2C+y%3D13x%2B2+
This is not a good example to use as "solve by graphing". It would be hard to tell that the x = -2/7 and y = -12/7 without doing the actual work.
To solve the system by graphing, we will graph the two equations on the same coordinate plane and find the point of intersection, if it exists.
First, let's rearrange the equations in slope-intercept form (y = mx + b) to make it easier to graph.
Equation 1: x + y = -2, can be rewritten as y = -x - 2
Equation 2: y = 13x + 2
Now, let's plot the graph of each equation:
For Equation 1 (y = -x - 2):
- Plot the y-intercept, which is -2, at the point (0, -2).
- Use the slope (which is -1) to determine the slope of the line.
- From the y-intercept (0, -2), move 1 unit to the right and 1 unit down to another point.
- Connect the two points to draw a straight line.
For Equation 2 (y = 13x + 2):
- Plot the y-intercept, which is 2, at the point (0, 2).
- Use the slope (which is 13) to determine the slope of the line.
- From the y-intercept (0, 2), move 1 unit to the right and 13 units up to another point.
- Connect the two points to draw a straight line.
Now, we can observe the graph to find the point of intersection:
The point where the two lines intersect is the solution to the system of equations. In this case, the lines intersect at the point (-4, -2).
Therefore, the solution to the system of equations is x = -4 and y = -2.
To solve the system of equations by graphing, we need to plot the graphs of both equations on the same coordinate plane and find the point where they intersect. This point will represent the solution to the system, where the values of x and y satisfy both equations simultaneously.
1. Start by rearranging the first equation, x+y=-2, to solve for y. Subtract x from both sides:
y = -x - 2
2. The second equation, y=13x+2, is already solved for y.
Now, let's graph both equations on the same coordinate plane:
- Choose a range of values for x, for example, -5 to 5, and plot various points for both equations. Alternatively, you can choose any range that you prefer.
- For the first equation, y=-x-2, select some x-values, substitute them into the equation, and calculate corresponding y-values. For example:
Let x = -3, then y = -(-3) -2 = 1 (giving the point (-3, 1))
Let x = 0, then y = -(0) -2 = -2 (giving the point (0, -2))
Let x = 2, then y = -(2) -2 = -4 (giving the point (2, -4))
- For the second equation, y=13x+2, choose a few x-values and calculate the corresponding y-values. For example:
Let x = -4, then y = 13(-4) + 2 = -50 (giving the point (-4, -50))
Let x = 1, then y = 13(1) + 2 = 15 (giving the point (1, 15))
Let x = 3, then y = 13(3) + 2 = 41 (giving the point (3, 41))
- Plot the points on a coordinate plane and draw a line through them for each equation.
- Identify the point(s) where the two lines intersect. This is the solution to the system of equations.
In this case, it might be helpful to use graphing software or an online graphing tool to accurately plot the points and draw the lines.
I can't graph if for you.
Plot these equaitons, and see where they intercepth.
y=-x-2
y=13x+2