If two linear equations are represented as ax + by = c and dx + ey = f, under wh

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Question: If two linear equations are represented as ax + by = c and dx + ey = f, under what condition will they be parallel?

Options:

Correct Answer: If a/d = b/e

Solution:

Two lines are parallel if their slopes are equal, which occurs when a/d = b/e.

If two linear equations are represented as ax + by = c and dx + ey = f, under what condition will they be parallel?

If two linear equations are represented as ax + by = c and dx + ey = f, under what condition will they be parallel?

Step 1: Understand that a linear equation can be written in the form ax + by = c.
Step 2: Identify the coefficients a, b, d, and e from the two equations: ax + by = c and dx + ey = f.
Step 3: Recall that the slope of a line in the form ax + by = c can be found using the formula -a/b.
Step 4: Write the slopes of both lines: the slope of the first line is -a/b and the slope of the second line is -d/e.
Step 5: For the two lines to be parallel, their slopes must be equal. This means -a/b = -d/e.
Step 6: Simplify the equation from Step 5 to get a/d = b/e, which is the condition for the lines to be parallel.

Slope of a Line – The slope of a line in the form ax + by = c can be determined by rearranging it to the slope-intercept form (y = mx + b), where m represents the slope.
Conditions for Parallel Lines – Two lines are parallel if their slopes are equal, which can be derived from the coefficients of x and y in their standard forms.