4.3 Exercises

1) Solve the following linear systems using substitution or elimination. Show all your work.

a) [latex]7x-4y=1[/latex]

[latex]3x+y=14[/latex]

b) [latex]2x-3y=-4[/latex]

[latex]5x+2y=9[/latex]

2) Kwazi had 13 coins, some nickels and some dimes. If the total value of the coins is 75 cents, how many nickels and how many dimes does Kwazi have? Solve this problem in two ways as follows:

a) Without using any variables and in a way that an elementary school student could understand. Draw pictures and explain your calculations. Clearly document any trial and error (guessing and checking) involved.

b) Using the substitution or elimination method. Clearly state exactly what each variable represents.

3) A bicycle store has many disassembled bicycles and tricycles. Altogether, there are 43 wheels and 17 frames.  If all the bicycles and tricycles were assembled, how many bicycles and how many tricycles would there be?  Solve this problem in two ways as follows:

a) Without using any variables and in a way that an elementary school student could understand. Draw pictures and explain your calculations. Clearly document any trial and error (guessing and checking) involved.

b) Using the substitution or elimination method. Clearly state exactly what each variable represents.

4) Create three different 2 by 2 linear systems for each of the following scenarios:

a) Exactly one solution

b) No solutions

c) An infinite number of solutions

5) Heidi weighs 4 pounds more than Grace. Grace weighs twice as much as Jen. The sum of all their weights is 58 pounds.  How much does each person weigh?

Let G represent Grace’s weight in pounds, H represent Heidi’s weight in pounds and J represents Jen’s weight in pounds.  Write three equations that would help you solve this problem.  Then try to solve it using a series of substitutions.  Don’t be afraid of some trial and error here.  Show your work below.