A system of linear equations has no solution when its lines are parallel but separate. Compare the variable coefficients: one multiplier must match both, while that multiplier must not match the constants. Desmos can confirm that the lines never cross. If the constant matches too, the equations describe the same line, which has infinitely many solutions.
Hints
- Hint 1
A solution to a system is a point that makes both equations true. If two equations have the same left side but different right sides, could any point satisfy both?
- Hint 2
Multiply the entire given equation by to make its variable terms match two of the options. What happens to the constant ?
Step-by-step
Match the variable terms, then check the constant
Step 1Graph the given equation
Type in Desmos. It graphs a line: every point on it satisfies the given equation. Keep it visible to check whether a second line crosses it.
- Step 2
Rewrite the equation to compare coefficients
Multiply both sides by : . This is still the first line. The multiplier applies to too, so the constant is . Matching variable terms with different constants give separate parallel lines that never meet.
- Step 3
Choose the separate parallel line
Add in Desmos. It shows two lines that never cross. At a crossing, the same expression would have to equal both and , which is impossible. So could be the second equation. Choice A.