Determine the number of solutions to this system of linear equations (0, 1, ∞): y=7x+8 −7x+y=−8 (1 point) This system of linear equations has solution(s).
To determine the number of solutions to the system of linear equations, we need to consider the relationship between the two equations.
The first equation, y = 7x + 8, represents a straight line with a slope of 7 and a y-intercept of 8.
The second equation, -7x + y = -8, can be rearranged to y = 7x - 8, which represents another straight line with the same slope of 7 but a different y-intercept of -8.
Since both equations have the same slope, but different y-intercepts, we can conclude that the two lines are parallel and will never intersect.
Therefore, the system of linear equations has no solutions.
To determine the number of solutions to this system of linear equations, we can use the concept of linear independence and the slope-intercept form of the equation.
The given system of linear equations is:
1) y = 7x + 8
2) -7x + y = -8
First, let's rewrite the second equation in slope-intercept form. To do this, we need to solve for y:
2) y = 7x - 8
Now we have two equations in slope-intercept form:
1) y = 7x + 8
2) y = 7x - 8
Comparing the two equations, we can see that they have the same slope, which is 7. Since the slopes are equal, the lines are parallel, and they will never intersect.
Therefore, the system of linear equations has no solution.