Which values of a and b make this system of equations have no solution?y=–2x+4y=ax+b
Question
Which values of a and b make this system of equations have no solution?
The equations are:
Solution
A system of equations has no solution when the two lines represented by the equations are parallel. Two lines are parallel when they have the same slope but different y-intercepts.
The slope of the first equation y = -2x + 4 is -2.
For the system to have no solution, the slope of the second equation y = ax + b must also be -2. Therefore, a = -2.
However, the y-intercepts must be different. The y-intercept of the first equation is 4. Therefore, for the system to have no solution, b ≠ 4.
So, the values of a and b that make this system of equations have no solution are a = -2 and b ≠ 4.
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