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.
