For a system of equations to have exactly one solution, the two lines represented by the equations must intersect at a single point. This occurs when the slopes of the lines are different.
To determine the slopes of the lines represented by the equations, we can write each equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
A. 2x - 3y = 6 can be rewritten as -3y = -2x + 6, or y = (2/3)x - 2. The slope of this line is 2/3.
B. 5x + 4y = 12 can be rewritten as 4y = -5x + 12, or y = (-5/4)x + 3. The slope of this line is -5/4.
C. -x + 2y = 4 can be rewritten as 2y = x + 4, or y = (1/2)x + 2. The slope of this line is 1/2.
D. -4x - 8y = 12 can be rewritten as -8y = 4x + 12, or y = (-1/2)x - 3. The slope of this line is -1/2.
Therefore, the equation that results in a system of equations with exactly one solution is B. 5x + 4y = 12.
When graphed on the same coordinate grid, which equation results in a system of equations with exactly one solution?
A.
B.
C.
D.
1 answer
1 answer