SAT Math Multiple Choice Question 282: Answer and Explanation
If the system of linear equations above has no solution, and a is a constant, what is the value of a?
Correct Answer: C
Category: Heart of Algebra / Systems of Linear Equations
Strategic Advice: Graphically, a system of linear equations that has no solution indicates two parallel lines or, in other words, two lines that have the same slope. So, write each of the equations in slope-intercept form (y = mx + b) and set their slopes (m) equal to each other to solve for a. Before finding the slopes, multiply the bottom equation by -3 to make it easier to manipulate.
Getting to the Answer:
The slope of the first line is and the slope of the second line is Setting them equal and solving for a results in