Digital SATMath: Advanced MathEasy
A project manager is tracking the progress of two teams. Team A's progress can be modeled by the equation y = 2x + 5, and Team B's progress by y = -3x + 20, where x is the number of days and y is the percentage of completion. At what number of days will both teams have the same percentage of completion?
- A5 days
- B2 days
- C3 days
- D4 days
Show answer & explanationAnswer & explanation
Correct answer: C. 3 days
To find when both teams have the same percentage of completion, set the two equations equal to each other and solve for x. This represents solving a system of linear equations.
Why the other options are wrong
- A. Substituting x=5 into the equations yields y=15 and y=5, which are not equal.
- B. Substituting x=2 into the equations yields y=9 and y=14, which are not equal.
- D. Substituting x=4 into the equations yields y=13 and y=8, which are not equal.
Solving Systems of Linear Equations by Substitution
To solve a system of linear equations by substitution, set the expressions for the dependent variable (if both are solved for it) equal to each other, then solve for the independent variable.
- Represents the intersection point of two lines.
- The solution (x, y) satisfies both equations simultaneously.
- Can be used when one or both equations are already solved for a variable.
Memory trick: Where two lines meet, the solution is sweet!