A linear equation is graphed on the coordinate grid below.
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
In order for a system of equations to have exactly one solution, the lines representing the equations must intersect at a single point.
Looking at the given equations, we can see that the slope-intercept form (y = mx + b) will help us determine the slope of each line.
A: -2x + 6y = -12
6y = 2x - 12
y = (2/6)x - 2
y = (1/3)x - 2
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
From this analysis, we can see that only option B has a different slope from the other equations, ensuring that the lines will intersect at exactly one point.
Therefore, the answer is B. 3x - 9y = 9.