Q5. Graph the following system of equation using slop and Y-intersept. Determine the number of solution for the system 3x=5y=-5, & 6x-10y=-10
+23254 Check the first equation: 3x=5y=-5; should it be 3x - 5y = -5?
If it is: 3x - 5y = -5 6x - 10 y = -10
-5y = -3x - 5 -10y = -6x - 10
y = (3/5)x + 1 y = (3/5)x + 1
slope = 3/5 slope = 3/5
y-intercept = 1 y-intercept = 1
Start at point (0,1) on the y-axis Start at point (0,1) on the y-axis
go over 5 and up 3 (place a dot) go over 5 and up 3 (place a dot)
repeat; draw a line. repeat; draw a line.
If the lines are parallel (slopes are equal and y-intercepts are not equal), they have no solutions.
If the lines are coincident (one in exactly the same place as the other) (slopes are equal and y-interceps are also equal), they have an infinite number of solutions, all the points that they have in common.
If the lines intersect (slopes are not equal), they have one solution, the point where they intersect.
The number of solutions is the number of points in which the two lines cross.
+23254 Check the first equation: 3x=5y=-5; should it be 3x - 5y = -5?
If it is: 3x - 5y = -5 6x - 10 y = -10
-5y = -3x - 5 -10y = -6x - 10
y = (3/5)x + 1 y = (3/5)x + 1
slope = 3/5 slope = 3/5
y-intercept = 1 y-intercept = 1
Start at point (0,1) on the y-axis Start at point (0,1) on the y-axis
go over 5 and up 3 (place a dot) go over 5 and up 3 (place a dot)
repeat; draw a line. repeat; draw a line.
If the lines are parallel (slopes are equal and y-intercepts are not equal), they have no solutions.
If the lines are coincident (one in exactly the same place as the other) (slopes are equal and y-interceps are also equal), they have an infinite number of solutions, all the points that they have in common.
If the lines intersect (slopes are not equal), they have one solution, the point where they intersect.
The number of solutions is the number of points in which the two lines cross.
