1.
a. Graph each equation.
x + 4y = 8
3x + 4y = 0
b. Determine the solution of the system of equations.
2.
a. Graph each equation.
y = 3x − 4
y = −3x + 5
b. Estimate the solution of the system of equations.
A. (1.5, 0.5)
B. (−1.5, −0.5)
C. (0.5, 1.5)
D. (−1.5, 0.5)
3. Renting a canoe to use on River Y costs $33. Renting a canoe to use on River Z costs $5 per hour plus a $13 deposit. The total cost, c, of renting a canoe, for n hours can be represented by a system of equations.
a. Which system of equations could be used to find out how many hours the canoe can be rented?
A. River Y c = 33
River Z c = 5n + 13
B. River Y c = 5n − 33
River Z c = 13
C. River Y c = 33
River Z c = 5n − 13
D. River Y c = 5n + 13
River Z c = 13
b. Graph the system of equations.
c. For how many hours could you rent the canoe at the same cost on both rivers?
4. The cost of endless chicken wings at Restaurant X is $10. The cost of chicken wings at Restaurant Z is 60¢ per wing plus a $1 charge for sauce. The total cost, c, of n chicken wings can be represented by a system of equations.
a. Write the system of equations.
b. Graph the system of equations.
c. How many chicken wings do you have to order for the cost to be the same at both restaurants?
5.
a. Writing Graph each equation.
x = y
2x = y − 3
b. Determine the solution of the system of equations.
c. Explain how to find the equation of a line that intersects the system of equations at the same point.
6. Reasoning The cost of making copies at Store W is $5 regardless of the number of copies. The cost of making copies at Store Z is 20¢ per copy plus a $2 charge for the use of the machine. The total cost, c, of making n copies can be represented by a system of equations.
a. Write a system of equations that could be used to find out the cost of making copies.
b. Draw a graph that shows the system of equations.
c. How many copies do you have to make for the cost to be the same at both stores?
d. If you have to make a smaller number of copies which store should you go to? If you have to make a large number of copies which store should you go to? Explain.