3.5 Sample test: 2 equations and 2 unknowns

Evan digs into his pocket to see how much pizza he can afford. He has $3.00, exactly enough for two slices. But it is all in dimes and nickels! Counting carefully, Evan discovers that he has twice as many dimes as nickels.

• A

  Identify and clearly label the variables.

• B

  Write two equations that represent the two statements in the question.

• C

  Solve these equations to find how many nickels and dimes Evan has.

Black Bart and the Sheriff are having a gunfight at high noon. They stand back to back, and start walking away from each other: Bart at 4 feet per second, the Sheriff at 6 feet per second. When they turn around to shoot, they find that they are 55 feet away from each other.

• A

  Write the equation $d=\text{rt}$ for Bart.

• B

  Write the equation $d=\text{rt}$ for the Sheriff.

• C

  Solve, to answer the question: for how long did they walk away from each other?

• D

  How far did Bart walk?

Mrs. Verbatim the English teacher always assigns 5 short stories (2,000 words each) for every novel (60,000 words each) that she assigns. This year she has decided to assign a total of 350,000 words of reading to her students. How many books and how many short stories should she select?

• A

  Identify and clearly label the variables.

• B

  Write two equations that represent the two conditions that Mrs. V imposed.

• C

  Solve these equations to find the number of works she will be assigning.

Solve by graphing . Answers may be approximate. (But use the graph paper and get as close as you can.)

$y=x^2-3$

$y=-\mid x\mid +2$

Solve, using substitution .

$\mathrm{3x}+y=-2$

$\mathrm{6x}-\mathrm{2y}=\text{12}$

Solve, using elimination .

$\mathrm{2x}+\mathrm{3y}=-\text{11}$

$\mathrm{3x}-\mathrm{6y}=4$

Solve any way you like.

$\mathrm{2x}=\mathrm{6y}+\text{12}$

$x-9=\mathrm{3y}$

Solve any way you like.

$\mathrm{2y}+\mathrm{3x}=\text{20}$

$y+x=6$

• A

  Solve for $x$ . (*No credit without showing your work!)

$\text{ax}+\text{by}=e$

$\text{cx}+\text{dy}=f$

• B

  Use the formula you just derived to find $x$ in these equations.

$\mathrm{3x}+\mathrm{4y}=7$

$\mathrm{2x}+\mathrm{3y}=\text{11}$