Estimate the solution to the system of these linear equations based on the graph. y=−5x+7 y=−2x+10 (1 point)
Based on the graph, it appears that the lines represented by the two equations intersect at a point. Therefore, the system of linear equations has a unique solution.
To estimate the solution to the system of linear equations based on the graph, we need to find the point where the two lines intersect.
The first equation, y = -5x + 7, has a y-intercept of 7 and a slope of -5. This means that for every increase of 1 unit in x, y will decrease by 5 units.
The second equation, y = -2x + 10, has a y-intercept of 10 and a slope of -2. This means that for every increase of 1 unit in x, y will decrease by 2 units.
By plotting these two lines on a graph, we can determine the point where they intersect. From the graph, it appears that the lines intersect at the point (3, -8).
Therefore, the estimate for the solution to the system of linear equations is x = 3 and y = -8.
To estimate the solution to the system of linear equations based on the graph, you can visually examine the point where the two lines intersect. This point represents the solution to the system.
The given equations are:
y = -5x + 7
y = -2x + 10
To find the point of intersection, you can plot both equations on a graph and look for the point where the lines meet. If you don't have access to a graphing tool, you can manually graph the lines by choosing some x-values, substituting them into the equations, and plotting the corresponding y-values.
1. Choose some x-values, such as x = -2, 0, 2, and substitute them into each equation to find the corresponding y-values.
For the equation y = -5x + 7:
- When x = -2, y = -5*(-2) + 7 = 17
- When x = 0, y = -5*(0) + 7 = 7
- When x = 2, y = -5*(2) + 7 = -3
For the equation y = -2x + 10:
- When x = -2, y = -2*(-2) + 10 = 14
- When x = 0, y = -2*(0) + 10 = 10
- When x = 2, y = -2*(2) + 10 = 6
2. Plot the points (-2, 17), (0, 7), and (2, -3) for the equation y = -5x + 7. Plot the points (-2, 14), (0, 10), and (2, 6) for the equation y = -2x + 10.
3. Draw a straight line connecting the plotted points for each equation.
4. Locate the point where the two lines intersect. This point represents the solution to the system of equations.
By visually inspecting the graph, it appears that the lines intersect at the point (2, -3). Therefore, an estimation of the solution to the system of linear equations is x = 2 and y = -3.