Exam 7: Systems of Equations

Solve the problem. -Kevin walks and jogs to his favorite coffee shop to study each weekend. He averages $3 \mathrm{mph}$ walking and $5 \mathrm{mph}$ jogging. The distance from his home to the coffee shop is $14 \mathrm{mi}$ , and he makes the trip in $4 \mathrm{hr}$ . How long does Kevin jog?

Solve by elimination. - $-2 x+6 y=-3$ $-8 x+24 y=-12$

Solve the problem. -Roberto invested some money at $6 \%$ , and then invested $\$ 5000$ more than twice this amount at $11 \%$ . His total annual income from the two investments was $\$ 4750$ . How much was invested at $11 \%$ ?

Solve the problem. -x+y=-11 X-y=3

Decide whether or not the ordered pair is a solution of the system. - $(-2,4)$ $\mathrm{x}+\mathrm{y}=6$ $\mathrm{x}-\mathrm{y}=-2$

Solve the problem. -The perimeter of a rectangle is $54 \mathrm{~m}$ . If the width were doubled and the length were increased by $17 \mathrm{~m}$ , the perimeter would be $104 \mathrm{~m}$ . What are the length and width of the rectangle?

Solve the problem. -A boat traveled for $3 \mathrm{hr}$ with a 3- $\mathrm{mph}$ current to reach a picnic area. The return trip against the same current took $6 \mathrm{hr}$ . Find the speed of the boat in still water.

Solve using the substitution method. - $x+y=12$ $\mathrm{y}=2 \mathrm{x}+3$

Solve by the substitution method. - $x+2 y=-8$ $2 x+3 y=-12$

Decide whether or not the ordered pair is a solution of the system. - $(-2,2)$ $4 \mathrm{x}=-6-\mathrm{y}$ $3 \mathrm{x}=2-4 \mathrm{y}$

Decide whether or not the ordered pair is a solution of the system. - $(1,3)$ $3 \mathrm{x}+\mathrm{y}=0$ $4 \mathrm{x}+3 \mathrm{y}=-5$

Solve the problem. -Ron and Kathy are ticket- sellers at their class play, Ron handling student tickets that sell for $\$ 1.00$ each and Kathy selling adult tickets for $\$ 3.50$ each. If their total income for 38 tickets was $\$ 83.00$ , how many did Ron sell?

Solve by the substitution method. - $x+5 y=7$ $-6 x+6 y=-42$

Solve the problem. -Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 20 coins with a total face value of $\$ 2.40$ , how many of the coins are nickels?

Solve using the elimination method. - $-x-5 y=-35$ $-6 x+5 y=70$

Solve by the substitution method. - $-5 x+7 y=-35$ $2 \mathrm{x}+2 \mathrm{y}=-10$

Solve by elimination. - $4 x-4 y=5$ $-8 x+8 y=10$

Solve by elimination. - $8 x-4 y=-16$ $4 \mathrm{x}+2 \mathrm{y}=-8$

Solve the problem. -A salesman sold $\$ 400$ more than the rest of the sales staff. If the sales total for the day was $\$ 1600$ , how much did the rest of the sales staff sell?

Decide whether or not the ordered pair is a solution of the system. - $(-5,3)$ $4 \mathrm{x}+\mathrm{y}=-17$ $3 \mathrm{x}+4 \mathrm{y}=-3$