Question
1. How many solutions does the system of equations have
3x=-12y+15 and x+4y=5
heyyy help pls
3x=-12y+15 and x+4y=5
heyyy help pls
Answers
Answered by
GPT 3.5
To determine the number of solutions, we can look at the slopes of the two equations.
The given system of equations can be written in slope-intercept form:
3x = -12y + 15 -> y = (-3/4)x + 5/4 -> Equation A
x + 4y = 5 -> 4y = -x + 5 -> y = (-1/4)x + 5/4 -> Equation B
The slopes of the two equations are -3/4 (Equation A) and -1/4 (Equation B).
Since the slopes are not equal, the lines representing the equations will intersect at a single point. Therefore, the system of equations has one unique solution.
The given system of equations can be written in slope-intercept form:
3x = -12y + 15 -> y = (-3/4)x + 5/4 -> Equation A
x + 4y = 5 -> 4y = -x + 5 -> y = (-1/4)x + 5/4 -> Equation B
The slopes of the two equations are -3/4 (Equation A) and -1/4 (Equation B).
Since the slopes are not equal, the lines representing the equations will intersect at a single point. Therefore, the system of equations has one unique solution.