Example Question - graphing method
Here are examples of questions we've helped users solve.
Solving System of Linear Equations by Graphing with Same Slope
To solve a system of linear equations by graphing, we need to plot each equation on a graph and identify where they intersect. The equations given are: 1) x + y = 2 2) x + y = 3 For each equation, we can solve for y to put the equation into slope-intercept form (y = mx + b). For the first equation: x + y = 2 y = -x + 2 (subtracting x from both sides) For the second equation: x + y = 3 y = -x + 3 (subtracting x from both sides) Now let's graph each equation. We'll start by plotting the y-intercept for each line, which is the point where x = 0. For the first equation (y = -x + 2), when x = 0, y = 2, so we have the point (0, 2). For the second equation (y = -x + 3), when x = 0, y = 3, so we have the point (0, 3). Next, we use the slope, which is -1 (since the coefficient of x is -1 in both equations), to find another point for each line. From our y-intercept (0, 2) for the first equation, move down 1 unit and to the right 1 unit to reach the point (1, 1). Similarly, from the y-intercept (0, 3) for the second equation, move down 1 unit and to the right 1 unit to reach the point (1, 2). Now, we can draw the lines through these points: For the first line: Draw a line through (0, 2) and (1, 1) For the second line: Draw a line through (0, 3) and (1, 2) However, upon examining these two equations, we realize they are parallel and have the same slope but different y-intercepts. Since they are parallel, they will never intersect. This means there is no solution to this system of equations; it is inconsistent. The graph provided in the image seems to be showing the lines incorrectly as they intersect, but that must be a mistake because, theoretically, the two lines cannot intersect given they have the same slope and different y-intercepts.
Solving System of Linear Equations by Graphing
The image shows a screenshot of a math homework problem asking to solve the system of linear equations by graphing: 1) y = x - 7 2) y = 2x - 2 To graph these equations, you need to plot at least two points for each line and then draw a straight line through these points. For the first equation, y = x - 7: - When x = 0, y = -7. The point is (0, -7). - When x = 7, y = 0. The point is (7, 0). Plot these two points and draw a line through them. For the second equation, y = 2x - 2: - When x = 0, y = -2. The point is (0, -2). - When x = 1, y = 0. The point is (1, 0). Plot these two points as well and draw a line through them. The solution to the system of equations is the point where the two lines intersect. By examining the graph that would be created, you can visually determine the point of intersection and that will be the solution to the system of equations. In the provided image, there is a small section of the graph visible, but to be precise, you would need to plot these points on a full graph, either on paper or using graphing software. The system's solution will be the coordinates where both lines cross each other on the graph. The exact solution can be found by setting the two equations equal to each other and solving for x, then using that x-value to find the corresponding y-value. However, since the task specifically asks to use the graphing tool, the solution should be obtained graphically.
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