Solve the system by graphing. Check your solution.
x = 7
y = -1
To graph the system, we need to plot the points (x, y) that satisfy each equation.
For the equation x = 7, we have a vertical line passing through x = 7.
For the equation y = -1, we have a horizontal line passing through y = -1.
The intersection of these two lines is the solution to the system.
Graph:
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Based on the graph, we see that the lines intersect at the point (7, -1).
To check if (7, -1) is a valid solution, substitute x = 7 and y = -1 into the original equations:
x = 7 : 7 = 7 (valid)
y = -1: -1 = -1 (valid)
Therefore, the system is solved correctly and the solution is x = 7, y = -1.
Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.
2x + y = 1
3y = 9 - 6x
To graph the system, we need to rearrange each equation in the form y = mx + b, where m is the slope and b is the y-intercept.
For the equation 2x + y = 1, we can rewrite it as y = -2x + 1. This line has a slope of -2 and a y-intercept of 1.
For the equation 3y = 9 - 6x, we can rewrite it as y = -2x + 3. This line also has a slope of -2 and a y-intercept of 3.
Since both equations have the same slope and y-intercept, they represent the same line. Therefore, the system has infinitely many solutions.