To create a linear system with no solutions, we need to construct two equations that represent parallel lines. Parallel lines do not intersect, so they have no common solutions.
Let's consider the following system of equations:
1) 2x + 3y = 6
2) 4x + 6y = 9
By analyzing the slopes of the lines represented by these equations, we can determine if they are parallel. To do this, we can convert the equations into slope-intercept form (y = mx + b) where "m" represents the slope.
Converting equation 1 into slope-intercept form:
2x + 3y = 6
3y = -2x + 6
y = (-2/3)x + 2
Converting equation 2 into slope-intercept form:
4x + 6y = 9
6y = -4x + 9
y = (-4/6)x + 9/6
y = (-2/3)x + 3/2
Both equations have the same slope (-2/3), indicating that their lines are parallel.
Since parallel lines never intersect, this linear system will have no solutions.
create a liner system that has no solutions
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1 answer