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, c is a constant. If the system has no solution, what is the value of c ?
Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.
ExplanationShow
The correct answer is 
. A system of two linear equations has no solution when the graphs of the equations have the same slope and different y-intercepts. Each of the given linear equations is written in the slope-intercept form, 
, 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-intercepts are 
and 
. Thus, if the system of equations has no solution, the slopes of the graphs of the two linear equations must be the same. The slope of the graph of the first linear equation is . Therefore, for the system of equations to have no solution, the value of c must be . Note that 1/2 and .5 are examples of ways to enter a correct answer.
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