Step-by-step explanation:
It's easier to graph when both equations are in its slope-intercept form, y = mx + b.
System 1:
-3x -15y = 15
-2x -10y = 10
-2x -10y = 10
-2x + 2x - 10y = 2x + 10
-10y = 2x + 10
-10y/-10 = (2x + 10)/-10
y = -1/5x -1 [slope: -1/5, y-intercept (0, -1)]
-3x -15y = 15
-3x + 3x - 15y = 15
-15y = 3x + 15
-15y/-15 = (3x + 15)/-15
y = -1/5x - 1 [slope: -1/5, y-intercept (0, -1)]
To graph this system, plot the y-intercept, (0, -1) on the graph, then use the slope, m = -1/5 (down 1 unit, run 5 units to the right). Repeat the process until you have enough points to connect and create a line.
Because the given systems of linear equations are equivalent, their lines coincide on top of each other. This means that they have infinitely many points of intersection. Hence, they have infinite solutions.
System 2:
8x + 6y = 24
4x + 3y = 9
8x + 6y = 24
6y = -8x + 24
6y/6 = (-8x + 24)/6
y = -4/3x + 4 [slope: -4/3, y-intercept (0, 4)]
4x + 3y = 9
3y = -4x + 9
3y/3 = (-4x + 9)/3
y = -4/3x + 3 [slope: -4/3, y-intercept (0, 3)]
Use the same techniques as described in the first part. Plot the y-intercepts on the graph, then use the slope of each equation to plot other points.
These lines are parallel, which implies that they will never intersect each other. Hence, there's no solution to this system.
Attached are the screenshots of the graphed systems of linear equations.
