Solve graphically.
x-y=0
y=x²
The reason I don't understand the question is the second equation with the x². How do I graph that? I'm not sure if I ever graphed with an exponent, and if I did, it was a long time ago.
Thanks!
Unless you have a typo, this is a very easy problem
Your first equation says that y = x
your second equation means that y = x^2
This is only true at (0,0) and (1,1))
Now:
y = x is a straight line in quadrants 1 and three at 45 degrees to the x axis
y = x^2 is a parabola, facing up (holds water) with vertex at (0,0)
other points at
(-3,9),(-2,4), (-1,1) (0,0),(1,1),(2,4),(3,9)
To graph the equation y = x², you can follow these steps:
1. Choose a range of values for x. Pick a series of values that will give you a good representation of the shape of the graph. For simplicity, you can choose values from -3 to 3.
2. Substitute each value of x into the equation and calculate the corresponding value of y. For example, if x = -2, then y = (-2)² = 4.
3. Plot the points (x, y) on the coordinate plane. For each (x, y) pair, locate the x-value on the x-axis and the y-value on the y-axis and mark the point.
4. Connect the plotted points with a smooth curve. Since the equation y = x² is a quadratic function, the graph will be a parabola that opens upwards.
Now, let's solve the given system of equations graphically:
1. Start by graphing the equation x - y = 0. This equation is in standard form, so it can be rearranged into slope-intercept form, y = x, by isolating y.
2. To graph y = x, choose several x-values such as -3, -2, -1, 0, 1, 2, and 3. Substitute these values into the equation to find their corresponding y-values. For example, when x = -3, y = -3.
3. Plot the points (x, y) for each (x, y) pair obtained in step 2. Connect these points with a straight line since the equation represents a linear function.
4. Now, graph the equation y = x² by following the steps described above.
5. The two graphs will intersect at one or more points. These points are the solutions to the system of equations.
By visually inspecting the graph, you can determine the coordinates of the point(s) of intersection, which represent the solution(s) to the system of equations.