Question: Which of the following pairs of linear equations has no solution?
Options:
x + y = 2 and x + y = 4
2x - y = 1 and 4x - 2y = 2
3x + 2y = 6 and 6x + 4y = 12
x - 2y = 3 and 2x - 4y = 6
Correct Answer: x + y = 2 and x + y = 4
Solution:
The first pair represents parallel lines, which means they will never intersect, hence no solution.
Which of the following pairs of linear equations has no solution?
Practice Questions
Q1
Which of the following pairs of linear equations has no solution?
x + y = 2 and x + y = 4
2x - y = 1 and 4x - 2y = 2
3x + 2y = 6 and 6x + 4y = 12
x - 2y = 3 and 2x - 4y = 6
Questions & Step-by-Step Solutions
Which of the following pairs of linear equations has no solution?
Step 1: Understand what a linear equation is. A linear equation is an equation that makes a straight line when graphed.
Step 2: Know that two lines can either intersect at one point, be the same line (infinite solutions), or be parallel (no solutions).
Step 3: Identify the slopes of the lines in each pair of equations. The slope is the number in front of 'x' when the equation is in the form y = mx + b, where m is the slope.
Step 4: Compare the slopes of the two lines in each pair. If the slopes are the same but the y-intercepts (the 'b' value) are different, the lines are parallel.
Step 5: Conclude that if the lines are parallel, they will never intersect, which means there is no solution for that pair of equations.
No concepts available.
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