Determine the number of solutions to this system of linear equations: y=x+5 y=−x+5 (1 point)
1 or 0 or 2 or infinite
The system of linear equations is:
y = x + 5
y = -x + 5
To find the number of solutions, we can compare the slopes of the two equations. The first equation has a slope of 1, and the second equation has a slope of -1. Since the slopes are not equal, the two lines will intersect at exactly one point.
Therefore, the number of solutions to this system of linear equations is 1.
To determine the number of solutions to a system of linear equations, we need to look at the slopes and y-intercepts of the lines.
The given system of linear equations can be written as:
y = x + 5 (equation 1)
y = -x + 5 (equation 2)
Comparing the coefficients of x in both equations, we can see that the slopes are different: 1 and -1.
Since the slopes are different, the lines are not parallel, and they will intersect at a single point.
Therefore, the system of linear equations has only one solution.
The answer is: 1
To determine the number of solutions to this system of linear equations, we can compare the slopes of the two equations.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
In the first equation, y = x + 5, the slope is 1. In the second equation, y = -x + 5, the slope is -1.
Since the slopes are different and the lines have different y-intercepts, the two lines will intersect at a single point. Therefore, the system of equations has one solution.
So, the answer is: 1.