Question Bank / Math / Systems of Linear Equations
Systems of two linear equations in two variables SAT question
Math · Algebra · Hard · Answer it here, explanation included.
In the system of equations above, a is a constant. If the system of equations has no solution, what is the value of a ?
ExplanationShow
Choice D is correct. A system of two linear equations has no solution when the graphs of the equations have the same slope and different y-coordinates of the y-intercepts. Each of the given equations is written in the slope-intercept form of a linear equation, 
, where m is the slope and b is the y-coordinate of the y-intercept of the graph of the equation. For these two linear equations, the y-coordinates of the y-intercepts are different: 
and 
. Thus, if the system of equations has no solution, the slopes of the two linear equations must be the same. The slope of the first linear equation is 2. Therefore, for the system of equations to have no solution, the value of a must be 2.
Choices A, B, and C are incorrect and may result from conceptual and computational errors.
Drill this skill on Aceit
Adaptive practice, a daily plan, and score tracking take a free account so we can save your work.
More Systems of two linear equations in two variables questions
- If satisfies the system of equations above, what is the value of y ?
- The system of equations above has solution (x, y). What is the value of x ?
- 32y-14x=23-32y 12x+32=py+92 In the given system of equations, p is a constant. If the system has no solution, what is the value of p ?
- Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4
- 5 x = 15 - 4 x + y = -2 The solution to the given system of equations is x,y. What is the value of x + y ?
- For the first line in the system: The line is horizontal. The line passes through the following points: (negative 4 comma 3) (0 comma 3) (2 comma 3) For the second line in the s