Replace the question marks by entering the coordinates of where the lines meet and press the Enter key. Then click “New Problem” for another system of equations.
Solving Problems with Systems of Equations.
(1.) Two friends live 7 miles apart. One Saturday, the two friends set out on their bikes at 8 am and started riding towards each other. One rides at 0.2 miles per minute, and the other rides at 0.15 miles per minute. At what time will the two friends meet?
(2.) Students are selling grapefruits and nuts for a fundraiser. The grapefruits cost $1 each and a bag of nuts cost $10 each. They sold 100 items and made $307. How many grapefruits did they sell?
(3.) Jada earns $7 per hour mowing her neighbors’ lawns. Andre gets paid $5 per hour for the first hour of babysitting and $8 per hour for any additional hours he babysits. What is the number of hours they both can work so that they get paid the same amount?
(4.) Invent another problem that is like one of these, but with different numbers.
(5.) Solve your problem.
Solving Linear System Equations Graphically.
In the applet below, note the system of equations displayed. One equation is displayed in pink. The other equation is displayed in purple.
Solve Linear Systems Algebraically.
Solve the pair of equations below by any method.
Here is an equation that is true for all values of : 5(+ 2) = 5+ 10. Elena saw this equation and says she can tell 20(+ 2) + 31 = 4(5+ 10) + 31 is also true for any value of . How can she tell? Explain your reasoning.
Consecutive numbers follow one right after the other. An example of three consecutive numbers is 17, 18, and 19. Another example is -100, -99, -98.
How many sets of two or more consecutive positive integers can be added to obtain a sum of 100?
A car is driving towards home at 0.5 miles per minute. If the car is 4 miles from home at t = 0, which of the following can represent the distance that the car has left to drive?