In order to have exactly one solution, the system of equations must have lines that intersect at one point. This occurs when the lines have different slopes.
To determine the slope of each equation, we can rewrite them in slope-intercept form (y = mx + b), where m is the slope.
A. -2x + 6y = -12
6y = 2x - 12
y = (2/6)x - 2/6
y = (1/3)x - 1/3
B. 3x - 9y = 9
-9y = -3x + 9
y = (1/3)x - 1
C. x - 3y = 6
-3y = -x + 6
y = (1/3)x - 2
D. 9x - 3y = 6
-3y = -9x + 6
y = 3x - 2
Comparing the slopes, we find that only equations A and B have different slopes. Therefore, the equation that results in a system of equations with exactly one solution is A. -2x + 6y = -12.
When graphed on the same coordinate grid, which equation results in a system of equations with exactly one solution?
A. -2x+6y= −12
B. 3x-9y=9
C. x-3y=6
D. 9x-3y=6
1 answer
1 answer